Basically, what I think it will come down to is one of two things. If voters are engaged on the issues in 2008, then I think she will do very well, as her issues are inline with much of center America. Of course, I am endlessly cynical about the odds of voters being engaged. Voters have already constructed a narrative of Hillary Clinton as an anti-family socialist leftist, and it will be tough to undo that.
So the other possibility has to do with how voters react to the campaign. Clinton is so despised by the rightwing that whoever their candidate is won't be able to stop the virulent attack ads even if he wanted to. Sullivan notes that
[Hillary can] still evoke almost pathological fury on the right. But that fury was most effective when it seemed to come from an excluded group, the beleaguered 'angry white men' of the last decade. Now that Republicans control every branch of government, too brutal an assault on Hillary might backfire.
If voters associate the assault on Hillary with the megalomaniac tendencies of the contemporary GOP, then the leftwing stereotype the right has worked so hard to construct will collapse and she may even become a sympathetic character. If that happens, I think she could put up quite a challenge.