Suppose not just one but several scattered tribes contributed leadership to the Continental Congresses and other Revolutionary organizations, so that at least two or three people from more than one tribe would be counted in a typical list of "Founders," and it would be well known that the majority of several tribes joined the Patriot side (as we Yankees call it anyway) of the ARW. And therefore, in an interaction between these separate tribes and the Anglo majority of Revolutionary and post-Revolutionary leaders, a solution was hit upon whereby all the Native peoples (who would be called "Indians," of course, and in the ATL where this scheme succeeds, the term has high status and is still used normally in modern times, so I use it here though I usually don't) retain control of an allotted, definite tract of land by technically separate treaties with the US Government, but are federated into an Indian Confederation which has its own central government elected by the tribes, and functions as a State in the Union for most purposes. That is, the Confederation gets two Senators in the Senate, a number of Representatives in the House depending on the rank of the combined Indian population among the states, two electoral votes plus the number of representatives for the President of the USA, and in Federal law is given a rank equal to other states, except in special matters where the Indians have special rights.
The Confederation is of course not geographically contiguous at all. With the Confederation participating in the US Continental government with a similar status to individual states under the Articles of Confederation, it is included in the Constitution of 1787 with an Article (or within the appropriate OTL Article) enumerating its commonalities with normal contiguous states and its peculiar rights and liabilities. Citizenship in the United States is automatically granted all members of tribes which enact a treaty of incorporation with the USA, and is explicitly stated to be devolved to the federal nation from their individual status as members of a native tribe--in other words, sovereignty is held to flow from individual rights "in a state of nature" via the tribe as a "natural" corporate entity to the USA due to voluntary federation. However, all Indian peoples engulfed in territory the USA claims by conquest or purchase or any other form of acquisition are required to incorporate their tribes by such a treaty.
The government of the Confederation is in principle left to the collective tribes members; that is, just as states determine voting qualifications and internal organization, the Confederation apportions voting rights to its central legislative bodies, and organizes intertribal relations as well as mediating between Indians and regular US citizens and other persons they might deal with on US soil.
Obviously, the attitudes and behaviors of "white" Americans would have to be different in the ATL for this to work, but the idea of the POD is that a substantial number of them recognize the Indians (those who allied anyway) as important members of the Federal union, and over time the political ebb and flow establishes the Indian Confederation as a crucial and normal part of the machinery of the USA, with the result that in general it and the Indian peoples it represents and governs weather the worst storms in notably better shape than OTL.
The theme of the thread is to incorporate particular Native peoples as States of the Union. One reason this would have been unlikely is that the demographics are generally against it, the largest Native groups being smaller than the smallest states. With the precedent established that consummation of union with the USA would involve statehood for individual tribes, the non-Native majority would find itself swamped out of power in the Senate, and despite the population of the separate tribes being much too low to ever have more than one Representative, the sheer number of them would also give them disproportionate power in the House as well, as well as in electing Presidents. The outcome of treating say just the Iroquois or the Cherokee as complete states would be to create an aversion to admitting any more Indian states, and attempts, probably successful, to disfranchise and abolish the already admitted ones, and at any rate other Native groups of much greater population than the established Indian states would not be admitted as such.
On the other hand, when I look at the statistics available for total Native American population (hardly any such is tabulated by the Bureau of the Census until 1900 however) it does seem that in all the years reasonably indicative data is available, the aggregate "Indian" population as reported is at any rate in the same ballpark as the smallest States of the Union by population.
Of course the very first Census was not until 1790, and for a hundred years after that Indians were not counted in any consistent way, precisely because until the late 1810s none of them were considered to be US citizens at all except by special and peculiar acts or circumstances. After 1817, tribes began to be admitted to US citizenship collectively. But even in later Census years when some Indians were counted, it would only be these (and probably not all of these) admitted as citizens, or residents of reservations who might have an intermediate status (technically citizens but exempt from many taxes and excluded from state and Federal representation). No attempt whatsoever was made to comprehensively census all Native residents of US territory until 1890; until then the shrinking "Indian Territory" (once, all the Louisiana Purchase west of the Mississippi, later most of the territory now comprising Oklahoma, then half of that--then none of it with Oklahoma statehood) was not counted at all.
In the ATL, the individual tribes, as they submit to being absorbed into the Union and incorporated into the Indian Confederation, do not get the vast, sweeping land grants initially conceded OTL--but neither do any of them get forced to relocate. All are granted Lands that are small by the standards of eary 19th century grants, but in proportion to the national per capita area of land available times their populations. And these Lands, once defined in treaty, are rarely if ever alienated from the tribe involved--unless it dies out, but even then the land does not revert to the Federal Government but is available for the Indian Confederation to allocate to peoples of other tribes. Because the leadership of the IC and most of the Tribal Lands will become accustomed to dealing with the general machinery of US society, by and large the Indians will be able to defend their right to what is left to them, and control interactions with the larger society so as to avoid worsening disruption. With the power of the scattered Indian peoples united in one body with state-like status but geographically spread all across the continent, Indians can offset their small and often collapsing numbers with other assets that they can use to advantage in the domestic politics of the USA and its transforming economy.
I would think that in these conditions, the demographic fate of the Native peoples will be somewhat less grim, and politically a much larger number of people would qualify and be counted as "Indians" that is possible or desired in OTL conditions.
First of all, while much of the demographic collapse of Native populations OTL was due to tragic circumstances involving the more or less inevitable introduction of Eurasian disease organisms to populations with no resistance, in a situation where the Indians have advocates with a vested interest in conserving their numbers, many contributing factors to the collapse can be offset or avoided. Intertribal warfare would cease, for instance. The wholesale disruption of the economic basis of traditional lives would be somewhat mitigated by large and definite land grants, and or explicit treaty rights such as hunting certain ranges while limiting or preventing Anglo citizens from overhunting or settling those lands. The Confederation would probably start organizing and sending aid to stricken communities early in the 19th century. They would advocate against sharp dealings taking advantage of the ignorance and naivete of small formerly isolated tribes who would in any case be protected better by treaties written under the influence and advice of the Confederation's agents. They would recognize that different Indian tribes have different concepts of property and territory and modes of government, and draft the treaties and design their interfaces with Confederation as well as Federal and neighboring state powers accordingly.
Also, in these circumstances, the Indians collectively have power. Not disproportionate to their share of population, but not less than that either. Individuals who OTL would seek to distance themselves from their Native connections for the sake of a better status in the dominant society might here choose instead to stress these connections, and it might be in Tribal and Confederation interests to encourage this. Even OTL tribes technically are responsible for determining their own membership; with their hands untied, it might well be that individuals with far too little blood connection to the people they claim, or unable to prove it with sufficiently reliable documentation OTL, might be welcomed in as either full tribal members, or a status that might be called "Friends of Tribe X" might be established for people with no plausible blood claims whatsoever but who are deemed valuable assets by the Tribe collectively.
Thus there would be a certain inflation, by OTL standards, of the status of Indian and thus their numbers.
If the demographic collapses of OTL can be mitigated so that say only 2/3 or half the number of people who died of disease OTL actually perish, and if other causes of premature mortality or high infant mortality can be addressed, the populations as we would count them OTL could be substantially larger, perhaps as much as doubled. Then, with tribes and the Confederation being lax about who can be counted as either an Indian or Friends granted more or less of the political and economic rights of Indians (but subject always to both Tribal and Confederation approval, with the Federal government having some say in the matter as well) we might be looking at 4 or 5 times the numbers of OTL in any given decade.
In the tabulations given after 1900, the lowest percentage of Indian populations given were in 1920 and 1950, at 0.2 percent of the total. Nowadays it is given at 0.9 percent--probably I would guess in part to the improvement of the social status of Native Americans, which causes more people to agree to be described as such. Surely also there is some improvement of quality of life to account for some of the increase--although that doesn't very well account for a proportional increase, especially since later decades of the 20th Century have also involved a fairly high rate of immigration. A lot of immigrants are from Mexico, but the definition of "native American" in the USA involves claiming connection to a people ancestrally resident in US territory, so the fact that many Mexicans and Central Americans do claim to belong to Native peoples would not apply to claiming to be an American Indian. Probably much of the actual demographic relative gain is because of poverty rather than wealth, with the general correlation of higher birth rates among poorer people. But I think clearly some of it is due to a higher rate of voluntary identification, fewer people dodging the label and more claiming it.
At one percent or less of the national population, the Indian Confederation would tend to have very few Representatives in Congress. Even so, at the modern figure of 0.9 percent, out of 300 million people that is 2.7 million, a population between New Mexico and Nevada, and thus would net the Confederation between 3 and 4 Representatives and thus 5 or 6 electoral votes for the President. At 0.2, the population would be 600,000--which is less than Vermont, but more than Wyoming.
Note that since incorporated Indian Tribes comprising the Conf ederation would always be counted as citizens but never as citizens of states, as long as the number of Representatives was being increased as states were added and populations grew (in the 19th century) the Confederation population would be counted (whereas most of the OTL people who would qualify were not counted by US censuses nor toward state appropriations) so the number of seats would have increased a bit more rapidly, and possibly been capped somewhat earlier. And today, once the size of the House has been fixed, the various states would have fewer seats to appropriate, while the Confederation would claim the balance.
If today, 5 times as many people claimed the identity of Indian as do OTL, and this claim were accepted by the interested parties, that would be 13.5 million people, or supposing the numbers we'd count strictly would be doubled, so there are 5.4 million we'd count, with 8.1 million others who would be denied the status by our rules, then if the ATL USA has identical population plus 2.7 million more Indians not eliminated, those other 8 million are a deduction from the net state populations. With 13.5 million, the Confederation would rank between Illinois and New York states--but it might rank higher still, in the fourth spot, due to the other states losing on average 2.7 percent of their populations. Of course we'd expect some unevenness, with the states farther to the west being notably less populous in terms of the non-Native populations they can count, and also lacking significant chunks of the territory they govern OTL, with considerably more than 3 percent of their land having been granted in perpetuity to numerous Tribes. Four Corners would probably not exist at all, with the respective corners of New Mexico, Arizona, Utah and Colorado being completely removed from any state jurisdiction, assigned piecemeal to various tribal people (mostly Navajo, but also tracts for Pueblo and some Apache groups). In addition to a huge Navajo tract with other peoples contiguous to it, lots of other large patches within and sometimes straddling OTL state borders would also be completely alienated from the various state governments--just as, to be sure, the Haudensee would enjoy autonomy in the Iroquois tract. All of these lands, be they small and densely peopled or sprawling and sparse, would be under the Confederation instead; even in New England the Praying Indians might be able to reassert their claims and get some autonomous land set aside within Massachusetts, Connecticut or even Rhode Island. So by and large, the Western states of this ATL will be relatively smaller in population and area than OTL, but even the Eastern states will give way a little bit.
Thus, the Confederation today might actually rank near the top, just below California, Texas and Florida, and be apportioned 27 or so Representatives. Obviously, the Confederation would long ago, from the first years of the current Constitution in fact, have learned the art of apportioning votes so that the very many Tribes included, far more than 27 and varying in size from a few hundred or less to hundreds of thousands or (given the multipliers of higher core populations and more fringe members being let in) millions. I can think of a number of methods that might be used in lieu of the simple matter of assigning groups of Tribal tracts to disjoint Districts; this might be one of many ways that the Confederation is not like a State at all.
What I lack is any information indicating the total Indian population that would have been included in the boundaries of the USA as defined by the Treaty of Paris--that is, the old 13 colonies plus what was called later "the old Northwest" and "the Old Southwest," these all being east of the Mississippi. Although some groups might possibly have grown, we have every reason to suppose the Native population between the Mississippi and the Appalachians would have been larger in 1783 than ever after OTL, and even in the ATL it will probably plummet before reaching a nadir sooner and higher than OTL, at a wild guess sometime in the 1850s or later. Even so, and bearing in mind that even before being massively disrupted by European invaders population densities were quite low compared to Europe or even the cores of the early settler colonies, it is a really vast, sweeping area and it is hard to believe that in the 15 states as of the apportionment of 1792 there were only a bit over 7000 Indians which the 0.2 percent demographic nadir would imply; it seems clear that even there there would be at least an order of magnitude more.
Farther west then, there must have been hundreds of thousands if not millions of Indians living west of the mountains, and they would exist in enough numbers that the Indian Confederation would be among the biggest "states," or perhaps the biggest bar none by a comfortable margin.
I suppose then that especially in the early years of the 19th century, the Federal government would put up roadblocks between the newly included peoples and full membership in the Confederation, to keep the Confederation in the middle or lower ranges of "state" power. Gradually though I suppose all Native peoples would gravitate toward incorporation into the Confederation, and hostile interests will only be able to slow this trend, not stop it.
So in the early days of the USA, before the Constitution and in the generation or two immediately after it is adopted, strong anti-Indian factions might try to limit the Confederation to just the few tribes that did aid the Revolution on the whole, and surely some of the Founders would oppose the existence of the Confederation. But others would champion it, and among them some individuals would be Indians from these and other tribes, so it goes through and gradually, slowly early in the 19th century but faster later, other tribes, including the remnants of some who were bitterly opposed to the USA, would come around to accepting the terms of incorporation and the Confederation would grow. As the rate of US population growth picks up from the already high levels of the Revolutionary era, due to increasing immigration combined with high rates of natural growth, there would be less concern to limit the size of the Confederation, which being a player in US politics would acquire a diverse mix of both allies and enemies, and indeed with internal factions most Anglo factions would have some Indians or other supporting them; few if any could afford to oppose them all as a bloc. The fervent demographic rise of the non-Native peoples will keep the electoral power of the Confederation in check, especially because of the terrible implosion of Indian population; by adding new tribes at a fast rate the Confederation might just barely maintain its population while around it old states and new alike surge up. By the middle of the century the role of Confederation advisors and envoys in mediating peace with the hitherto undisturbed peoples in the west might be generally valued across most partisan lines, and liquidation of the Confederation would be unthinkable politically.
The more successful the Confederation is in bringing the tribes under its wing to some sort of workable accommodation with the modernizing world around them, the sooner the demographic collapse stops and reverses, and the entity will begin to keep pace with its rank in the list of states by population. In the 20th century I expect it would start rising again steadily; by then all the surviving tribal peoples would be "in."
With this kind of power, I suspect that before the end of the 20th century, at least one US President would be from the Confederation, and Indian Justices of the Supreme Court probably would have been appointed before 1900.