Survey says 98 out of 100 senators think they should be president. Frist is not one of the two who don't.
But his chances are slim, and he may just be smart enough to know that. He has no star power. He has no signature issue except healthcare, and he has not staked out an conservative position there.
Worst of all, from my point of view, is that he went to Washington with no coherent political/economic philsophy, because he had been a doctor his whole life and paid scant attention to such things. As a result, what philosophy he does have in those areas was shaped by the Washington elite, and will have no resonance with mainline Republican voters.
My guess is the two Senators who don't think they should be President are McCain and Clinton. Am I right? :P