NY Post gives her 20-1 odds:

Paterson, who confirmed Friday that he had discussed the Senate job with Caroline, was described as "liking and respecting" the last remaining child of former President John F. Kennedy, as well as seeing her as an "enormous potential drawer" of contributions to his own planned campaign for governor in 2010.

But the governor, who has the sole authority to name a new senator, was also said to be concerned that Kennedy, whom friends call "quiet and non-assertive," doesn’t have the personality to be an aggressive fighter in the Senate on behalf of the state’s increasingly desperate need for federal financial help.

"The bottom-line question is: Can Caroline Kennedy be the tough, hard, calculating, aggressive, articulate and, yes, obnoxious type of senator New York needs and expects?" said a second administration insider.

She’s proven she can kill an unflattering story and pull strings to get Rupert Murdoch’s kid into private kindergarten, so she’s no stranger to exercising power.  But I’ll feel a bit better about the idea of another Senator Kennedy when she hits the road in upstate New York, presses the flesh with voters, listens to their concerns, answers their questions and proves she can stand up to the rigors of the campaign trail.