McCain was
really pissed at George W. Bush after 2000, and it led him to compile the most liberal voting record of his career in 2001.(*) Now, to be fair, that was
still right-of-center -- but no more so than, say, Arlen Specter. There was considerable chatter inside the Beltway that the Democrats were eyeing McCain as a potential target to switch parties.
Obviously, 9/11 threw a monkey wrench into those plans, particularly in that McCain's military views aligned with the neocons on the ascendancy in the Bush White House. McCain drifted slowly more rightward, and -- as you know -- endorsed Bush in '04 and declined John Kerry's offer to be VP.
Without 9/11, I could envision McCain continuing to drift leftwards and actually switching parties sometime during the Bush presidency. That would not make him a viable presidential candidate, but he would certainly be attractive to Democratic nominee Barack Obama for all the same reasons that Joe Biden was chosen IOTL (white, gravitas, foreign policy experience, popular with blue-collar rural Dems, etc) and then some.
Of course, absent 9/11, I think Bush probably loses the White House in 2004 (to, probably, Kerry/Edwards), so you're looking at Obama/McCain 2012 rather than 2008. And, to be honest, a large part of Obama's support among Democratic primary voters was by being "not George W. Bush"; in a world in which Bush is the Republican equivalent of Jimmy Carter instead of being perceived as the embodiment of evil, there's probably not the same liberal groundswell for Obama as your nominee.
So the bottom line is that it's incredibly unlikely; but hey, I think you probably knew that when you asked.
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(*) And then, after losing to Obama in 2008, McCain promptly racked up the most
conservative voting record in his Senate career. Why, it's almost as if his driving force is bitter hatred for the guy he just lost to, as opposed to any particular political principles.