For Hillary to challenge a sitting black President would be a lot trickier. Short of Obama announcing he won't run for another term (extremely unlikely) I don't see her running in 2012.
I guess Teddy smelled blood, figured Carter wasn’t liberal enough, thought enough time had passed since Chappaquiddick, and decided to go for it. He didn’t do that poorly winning most of the big states including NY and CA and nearly 40% of the delegates.
Of course Teddy could have never won a national election carrying more personal baggage than a 747.