Why not, indeed? She is a Harvard law professor who would drive Republicans crazy, but put them in a box since she is so anti-Wall Street. Of course, Fox News will just make up some lies, and the rest of the media would repeat them as gospel, but it would be cool to consider her.
http://voices.washingtonpost.com/ezra-klein/
So there's a case that the Obama administration should pick someone who Democrats will really like and who the public is likely to eventually support. I think someone well known like Clinton actually makes sense from that perspective. Another unlikely idea: Harvard Law professor and financial regulation expert Elizabeth Warren, whose appointment would be an admission that many of the Court's most consequential decisions are on economic and regulatory matters, rather than just on the cultural issues that tend to dominate nomination hearings. Warren is primarily controversial because she's pretty tough on Wall Street, which may not be a fight the GOP wants to pick right now.
That said, the point of this post isn't to toss out clever names, just to make the point that the conventional wisdom that Obama should avoid a fight here might be wrong. He's likely to get one whether he likes it or not, and the question is more whether it'll be a fight that his supporters want to be part of.