I think most Americans on seeing a picture of Obama will say "That's an African American". They won't say "Oh, he's bi-racial" because his features are more black than white.
On looking at a picture of (say) Leona Lewis, most people would say, "She's bi-racial' because she looks neither black nor white (just beautiful - lucky girl).
Anyway, that's all semantics - and as for the Southern states of America - well, if you look at the polical map of America, they're traditionally Republican states, so whether the Democrats put up a black man, a white woman or a large suet pudding, it won't really make that much difference to the way the electoral colleges vote.