I've said it before every time this thread comes up, and I suppose I'll have to say again here. The best chance for any native state in North America is the Mayan Free State. They rebelled from Yucatan (which had just rebelled from Mexico) in 1847 and continued to rebel until the last village was taken in 1933. They came very, very close to winning in 1848 when they had the Yucatecan capital of Merida, the last remaining white city in the area, under siege, but broke it off due to the harvest time coming. Even then, it was not a unanimous decision. Just that enough of them left that the leaders and the others realized they couldn't take it on their own and went back too. If more stayed, Merida would have fallen and Mexico would be completely unable to regain control over the Yucatan. And there you go, a country ran by natives and probably gaining recognition from Britain.
True Yucatan is the most likely to become a North American Native State, but depending on when the POD takes place and the butterflies it produces, there are actual chances in having other Native American in North America and the US.
Assuming the 13 colonies break off into independent republics expansion westward would probably go slower and it would be unfeasible for any of them to expand past the Mississippi if they are fighting each other and Britain for the territory. In such a scenario I can see several Native or semi-Native states emerging.
By the Great Lakes
Tecumseh's Confederation (Indiana/Illinois) - Set up by Britain and its "allied tribes" as a buffer between British North America and an expanding New York, Pennsylvania and Virginia. I am not sure how much the first two wanted to expand but if Virginia tries to reach the Great Lakes; Britain will likely try and set this up.
The South East
Florida - a Seminole state with other south-eastern tribes (likely most of the civilized tribes) that will probably be pushed away from their lands by expanding Virginia the Carolinas and Georgia.
The Four Tribes (Alabama Mississippi) - They manage to work together and play the ex-colonies well enough that they retain independence.
Greater Georgia (might include West Florida) - Georgia expands and respects native lands and property. Georgia becomes both a white and native nation.
Arkansas (Includes Oklahoma)- Tribes are pushed west. They end up on the other side of the Mississippi and start their confederation there.
The West
Lakota/Dakota - with slower expansion westwards. They might be able to get a deal between Britain and whoever controls Louisiana into getting their own state. The state might grow smaller and smaller as settlers invade the West but if they survive long enough, without a great power they might be respected.
Comancheria - There might be white settlement in Tejas and it still might get its independence from Tejas. If Mexico also balkanizes well west Texas might get its own deal (very unlikely).
Navajo - Very populous (relatively) isolated form the rest of Mexico by dessert. if things in Mexico go very sour, like Yucatan they might decide at one point to get their own deal.
However in order to have any of the above you really need a drastic change, like not having the thirteen colonies unite, or Georgia not joining in during independence. New England splitting off early on and the rest of the US not being able to get its act together quickly.