The inability of the Republicans to beat a weak establishment candidate like Gore would effectively doom W from trying again. Gore was never seen as very strong, and even a close race in 2000 would confirm the conventional wisdom that W must've been particularly weak to lose. His allies would abandon him.
While McCain would be the clear frontrunner from day 1, the timing of events would probably lead Jeb to give it a try. Bush fatigue would be more of a factor, and it's possible McCain tries a post-midterm pivot to the right to scoop up the Bush neocon alliance.
Also obstructionism would be a hard sell, at least from 2001-03. If the results are the same (or similar) you've got a 50/50 tie in the senate and a Republican majority in the house of about four. Nobody can manage caucuses with that math to complete obstruction. Besides, you've got a very motivated McCain in the senate looking to make a lot of bipartisan deals to bolster his own "maverick" image. And the idea of completely shutting down the government was only considered as a reaction to Obama's election. I highly doubt the close election of Gore would prompt such a move.
McCain might still try to pivot the right after the midterms to forestall major competition in the presidential primaries, but I'm iffy on his chances with Jeb running. I'm pretty convinced that Jeb can keep the W alliance together, especially in the face of a McCain with even more questionable conservative credentials.
After the midterms, the GOP would certainly have strong majorities in both houses. If they don't experience a large wave, I would be very surprised. At that point the agenda gets more conservative and it's questionable whether Gore would be willing to negotiate. Especially if any successful legislation can be spun as a victory for his probable challenger. But then not doing anything looks bad for him, too.
The nature of the Republican wave in 2002 is very important. The most likely scenario is that they win big with a traditional push to the right. But without the solidification of the neocon movement in 2000, TTL doesn't really have a single Republican brand yet. It's unlikely that a weak figure like Gore would prompt a strong reaction like the Tea Party movement. It's possible that a narrative emerges from 2000 that McCain's supposed pragmatism would've been a better strategy, seeing more McCain-like candidates gain success as moderates abandon the Democrats for something new and bring their preference for heterodoxy to the GOP.
A traditional conservative wave likely means McCain pivots to the right after the midterms. A more heterodox wave likely means he stays the course and takes leadership of this new, rising faction.
A pivoting McCain still likely has to swat Jeb down in the primaries; a non-pivoting McCain definitely does.
A pivoting McCain can pick whomever he wants as a running mate; a non-pivoting McCain has to pick a true conservative. Either way, he's not nearly as pressured to pull someone out of left field since anyone he picks looks fresh next to Gore/Lieberman.
Barring a war or major terrorist event, McCain wins easily. I'm still in the camp that thinks he wins even with war/terrorism in the mix, but I disagree that such an event would make things worse for Gore. The incumbent would certainly be aided under those circumstances. But another term is just too much to ask the American people.
As for 2008, it's probably too far to tell. There's certainly no reason the housing crisis might not happen a few years earlier or later. If it happens just on schedule, McCain is in big trouble. Early in his term and he probably won't even get blamed for it. If it happens in his second term, well, he owns it but it doesn't matter to him electorally-speaking. There's even a chance Gore provokes it super early just by having better investigators poking into things, in which case he gets totally destroyed in 2004. It could even get so bad that he doesn't run for reelection.
Having Gore around doesn't stop Hillary from entering politics, but it could keep her from ever being able to run for president. Gore could well squeeze all the possible remaining juice from that brand.