One huge problem that most people aren't addressing is the fact Natives are numerous cultures, languages, religions, with each their own varying levels of complexity in social structure and internal dynamics. Yes there are commonalities and shared traditions across tribal lines, but even here there are several distinct cultural spheres that only interacted at their frontiers before contact. Not to mention the sheer differences in development that occurred during the 500+ year period of the Post-Colombian era.
At what point are you proposing such a pan-tribal nation form? And where? Focusing on what would become the Anglosphere, during the early years, there's a chance to save the complex and more urban centered Mississipians, such as them getting access to superior strains of Mesoamerican corn and domestic animals from Europe before they faced societal collapse from their own short comings and the Eurasian pandemics. Here you could see an empire or confederation arise that would be capable over time to field armies and adapt more complex European technology.
After this, things get much more difficult. Given different colonial claims, which create more competition and space for buffers and proxy forces, you could see the indigenous equivalent of Thailand and India-style princely states develop, or at the very least more autonomous areas like the original Indian territory that would become Oklahoma. If there was perhaps more competition out west, such as a stronger New Spain/Mexico, or somehow Russia manages to settle/control more or some other colonial development that starts on the west coast and moves east, the plains tribes could become buffer communities that hold onto claimed territories of various states/colonies, somewhat like how Russia and China conquered Central Asia; maybe some form of an alliance could form and remain a neutral Afghanistan-style buffer, and eventually build up their tech and social complexity.
Or going into Pre-Colombian PODs, you could have more complex societies develop or have more domesticated animals like in such TLs as Twovultures'
Peccary Rex and Dvaldon's Thule empires in the arctic. Another possibility is to have a more united and sophisticated society develop amongst the Pacific Northwest tribes. Or beyond the Anglosphere there's always Mesoamerica and the Andes empires and states (and here's my shameless plug for my TL
).
But the ideas of a "Senate of Chiefs" and just growing potatoes and worshiping Jesus is not going to cut it. It's rather childish, artificial, and naive, and displays an ignorance of the actual dynamics and diversity of the Americas' indigenous peoples. And even with the common AH trope of the Iroquois siding with the early US isn't going to cut it. By this point we were internally divided between religious camps, personal ties between both Patriots and Loyalists, along with societal decay from enclosure on lands and fading influence, credibility, and economic output out west. Basically we were on our last leg by the ARW. Not to mention as well that the Haudenosaunee remained neutral during the ARW until Sullivan's Trail. Only individual bands supported either side before this, and created a civil war amongst the league. After our homeland was burnt to the ground,
regardless of previous aid rendered to the Americans by certain tribes and individuals, it was only then we wholly sided with the British. This was also because the British told us that we'd only get food and refuge if we fought for them. Plus it wasn't the British authorities that were threatening to steal our lands, it was the Americans. At best if somehow we were convinced to side with the States, it would most likely just be larger reservations.