Oh no, I completely understand wanting to keep the US intact, if only for some time. There's always a point at which a country grows tired of fighting, especially with themselves. Hell, we don't even need the Natives to succeed in achieving independence; it's simply their goal, one that may not actually be achieved. It would be interesting to see only a resurgence of Native resistence, as opposed to either side succeeding.
Not saying you're wrong about the rather small size of the Native population, but I think there's more that should be taken into account.
1. The Natives would seek to establish communes. This would be a rather welcoming idea to leftists in the US--and with both the leftist remnants of the past wars and the rise of conservatism, the idea of a vast expanse of communes would be a welcome sight. If there wouldn't be leftists joining the group, there'd still be some amount of support.
2. International aid. No doubt some governments would be interested in a left-wing independence movement, be they for or against it. This can be game changing for both sides; say, if the Spanish aided the US in stopping the movement, or the Chinese aided the Natives.
3. Guerrilla warfare can be a powerful method--and who else to take part in it than the Native Americans?
4. The past few conflicts have exhausted the whole damn continent--though I guess it's ultimately up to you to decide your country's military power.
Forgive me if I sound condescending; in all honesty, that's not my intent, and I hope that's not the effect. Again, this is just to suggest that this goes beyond population. You're most likely right, in that on their own, they may not get very far. It is for this reason that they would likely seek international aid or attempt to swell their numbers by receiving a large influx of leftist supporters across the country. The latter would, of course, be a decision entirely up to you--one which I am sure you wouldn't permit ;)
I'm not gonna make a guess at the numerical size of the natives; that's another fact that'd be up to you.
Assuming this faction gets allowed in at all, are there any ground rules you'd have about their existence? They are in your country, after all.