So
I wrote about this two years ago. I argued that in the context of the times, McCain could well have been the Democratic presidential nominee in 2004 (regardless of whether he formally declared himself a Democrat or continued to be an independent, a la Bernie Sanders).
I got a lot of understandable pushback on that, but I continue to think it was plausible. In the early 2000s, there was a broad centrist political consensus over domestic policy (with Republicans of course more enthusiastic about tax cuts and Democrats pushing for more incremental increases in the social spending and non-financial regulation). And there was a broad spirit of pragmatism within the party and even on the left, which felt fairly marginal.
McCain's voting record actually swung considerably to the left in the first Bush term, with McCain co-sponsoring virtually all major Democratic bills, including things like cap-and-trade proposals, drug re-importation, and background checks on guns. Notably, his top political aides at the time, Marshall Whitmann and John Weaver, both (for a time) switched party registration.
Moreover, the Democratic Party mood throughout the 2000's was so anti-Bush they were willing to welcome virtually any former Republican who would criticize Bush. Jim Webb was considered a star when he first won in 2006, especially in the left "blogosphere" and a lot of people pushed for him to be the 2008 vice presidential nominee. Especially given that McCain had already moved left in 2001, I suspect his past transgressions would be largely overlooked. Not true in today's climate, mind you, but in the mid 2000s that wasn't as clear.
One major objection that gets cited is Democrats' opposition to the Iraq War. McCain was an avid supporter of the intervention, and many asked why his imagined 2004 campaign wouldn't suffer the same fate as the OTL Joe Lieberman campaign. The difference here is that Lieberman didn't just back the war - he outright pushed back on virtually any criticism of the Bush Administration over it, downplayed revelations of torture, and spent his campaign largely attacking the Democratic left. McCain was OTL actually far more critical of the war's conduct than Lieberman. And OTL Democrats did nominate John Kerry, who also refused to repudiate his vote until quite late in that campaign (September 2004).
Now, to be clear, I don't predict at all smooth sailing. A lot of McCain's fawning press coverage would dissipate once he was just a Democrat, not a renegade Republican. And though I think he well could have been the party establishment's choice for the 2004 nomination, he would have gotten pushback from some of the base. I imagine he'd have a more drawn out primary win than Kerry did, for example. And I imagine the relationship between John McCain and the Democratic Party would sour quite quickly post-2004 win or lose.
If he wins, McCain would likely appoint Clintonites to a lot of staff and cabinet roles, but his inner circle would be dominated by his personal loyalists. Like him, mostly former Republicans. He'd be considered a traitor from the Republican Congress and would get zero congressional support for anything. Meanwhile, his own executive actions would likely fall short of what even the center-left Democratic policy establishment wanted. He'd quarrel with labor, most Democratic interest groups, and his own aggressive tack abroad would alienate him from a lot of Democratic rank-and-file even before the financial crisis hits.
So I imagine an unhappy term, with him quarreling with both parties, and I could see him leaving the party post-presidency. If, for example, a 2009-2013 Romney term is followed by an Obama presidency, easy to imagine McCain emerging as an Obama critic and declaring himself an independent again.