Here's a graph of the 50 states with the length of the bars equal to the percentage of the population that is nonwhite as of the 2010 Census. States that went for Obama in 2012 are in blue, while states won by Romney are in red. (Romney's share of the two-party vote appears following the name of each state.)
Perhaps surprisingly, when you graph it out state by state, the red-blue divide isn’t all that clear. At the top of the chart are the whitest states, Maine and Vermont, which Romney lost in landslides, then West Virginia (which Romney won), New Hampshire (Obama), North Dakota (Romney), and Iowa (Obama). Not much of a pattern.
Overall, though, you can see a little more Republican red toward the top in the whiter states and a little more Democratic blue toward the bottom in the least white states.
I put this graph up here to show that this is the kind of hodge-podge you normally see when you graph a single factor that impacts voting at the state level. The world is a very complicated place, so it's hard to come up with any one factor that sorts the blue states from the red states.
Except ... take a look at this graph.