Clinton's comparative advantage over Obama is with women, working-class whites, and Hispanics. Adding her to the ticket would be a move aimed at strengthening Obama's prospects in Virginia and in eastern Big Ten Country -- Michigan, Ohio, and Pennsylvania. All of these states hinge on moms and working-class whites.
Hispanics are the wild card. The Obama Administration hasn't done much to advance immigration reform, and this is probably a zero-sum game in the short-run. It's possible that Clinton might be able to shore up Hispanic support in Florida, Colorado, and Nevada.
The Obama camp can kiss North Carolina and Indiana goodbye, states it won ironically thanks to fierce primary battles. The president won many moderate Republicans in those two states and in Virginia, but he's not going to hold them in 2012, and there's nothing Clinton or Obama can do about that.
The map below from MyDD isn't a perfect indicator of where Clinton would boost Obama, but it's a good one. Ultimately, adding Clinton to the ticket would probably serve more as a shot in the arm to the Democratic base than as an appeal to win back "soft" 2008 votes.
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