Matthew Yglesias predicts that, as the country grows more non-white, white voters will grow more Republican:

I used to hold to the view that the growing non-white share of the electorate would, over time, tip elections to Democrats. I now think the system will remain near equilibrium and what we’ll instead see is white voters growing more Republican as Democrats are more and more seen as the party of non-whites. Mississippi and Arizona, after all, have very large minority votes but they’re hardly hotbeds of liberalism. Instead they’re hotbeds of very conservative white people.

I don't think these examples are very useful. The white vote in Mississippi is, well, from Mississippi. The white vote in Arizona is disproportionately old.

Yglesias's thesis is that future generations of white voters will be growing progressively more Republican. But right now, young white voters are dramatically more Democratic than older white voters. Thus the massive Democratic supermajorities among the young. Not only is the younger generation less white, but the whites themselves are more liberal:

White voters over 30 broke for John McCain by 16 points in 2008, while white voters under 30 went for Obama by 10 points. For Yglesias's thesis to be born out, those white voters would have to undergo a massive pro-Republican shift as they age -- not only getting more Republican, but getting more Republican than current old white voters are right now.

That seems unlikely. It seems to me that the choices really are that Republicans will achieve parity among Latinos -- which probably depends upon getting them to identify with the whites and against the blacks -- or else Democrats will have a general working majority, interrupted by recessions, scandals, and whatnot.