Interestingly, there’s talk of a Chuck Hagel (anti-war conservative) third party candidacy in 2008, possibly on a ticket with Mayor Bloomberg, which makes sense for Hagel since he wants to run, is a long shot to win the Republican nomination and anti-war positions rile the Bush faithful. That would make it more difficult for Giuliani to run as a third party candidate, which is, according to polling expert Charlie Cook, his best chance for winning.
Giuliani leads polls for the general elections and for Republican primaries, but speculation is that if he ran as a Republican his centrist positions on abortion and gay rights, as well as tales of his corruption, would stick to him and he would nose dive in the polls. McCain seems to want Rudy in the race, since that would be more cause for conservatives to rally around him, while a one on one race against a conservative (Romney or Brownback) could end badly for him. This is hard to picture for people who aren’t xenophobic but one way to look at it is to look at all the people who voted for Bush against McCain in 2000, and guess how many of them would vote for McCain or Giuliani in 2008. My guess is not too many.
Any Republican third party candidacy would be good for the Dems and thus the nation. After watching African-American congressman Harold Ford get beat for Tennessee Senate by an attack ad with guys in blackface and naked white women scripted by a guy that was later hired by McCain, I am inclined to think Barach will need this kind of help to win the battleground Bible Belt states (TN, Missouri, Arkansas) though he could win without them if he gets the Midwest and Florida.