I would eliminate John McCain from consideration. Conventional wisdom may indicate that he's the "most popular politician in America," but that's really nothing more than media hype. He was the most popular politician in America as long as the media propped him up as an "anti-Bush" type of political personality, but this media love-fest will end the moment he gets a GOP nomination for President. In fact, I would guess he'd be lucky to get 45% of the popular vote against most Democrat candidates.
I don't think McCain's popularity is a creation of the media at all, I've been too many places and heard it from too many people. Whatever we think of him the eveidence shows he's a powerful figure and should be used accordingly, in a Bush cabinet position, IMO.