Aren't African American voting turnouts fairly low? Maybe I'm talking out of my butt here, but if they came out in force and voted in high numbers, I think they could actually make a significant enough difference.
A large part of the problem is that fewer African-Americans vote, which isn't always entirely down to laziness. It's harder for various reasons to vote if you're black, or working-class for that matter. That is particularly the case in the South, where African-Americans are more numerous anyway.