the kind of fantasy history revision game that gets spawned from these digressions. So I'll bite.
It probably hinges on 9/11: whether Gore was able to (give the appearance of being able to) stop it from happening, or if he wasn't, assume a tough guy posture and execute a military response, like W. I doubt whether Gore would have invaded Iraq, of course; that was its own Bizarro World one-off.
(I don't think, having lost the presidency in the Supreme Court in 2000, that George W. Bush would have ever sought the presidency again. But we might have seen Jeb pop up a lot sooner than 2016.)
Let's assume 9/11 happens as previously scheduled, historically. Gore gets blamed for being lax, and unlike Bush, does not start a war in Iraq but does go after Osama bin Laden in Afghanistan and does not capture or kill him prior to November 2004. In other words, history unfolds essentially as it actually did, without Iraq as a backdrop or distraction. No Abu Ghraib, no yellowcake in Niger, No Dick Cheney, no Scooter Libby outing Valerie Plame, etc.
Just 9/11 and no Osama in hand nor at the bottom of the sea, as it was thirteen years ago.
I would say more than likely, in this scenario, you would have seen John McCain sworn in as president in 2004. That the winning argument was: we need military men in charge in order to prosecute this War on Terra, or some such.
Extend that out and a Vice President Hagel would have eventually been a GOP nominee for president, perhaps in 2008 as MCCain retired but almost certainly in 2012. Hagel would be very difficult to defeat, given his prior four (or eight) years as VP. We might even be sitting in the middle of Hagel's second term, an unprecedented 13-going-on-16-year run for the GOP (only 12 years of Reagan-Reagan-HW Bush in the '80's and early '90's comes close in the modern era).
Pretty demoralizing for the Democrats, through that lens. More importantly, Senator Barack Obama of Illinois might still be waiting his turn, and no one had ever heard of Sarah Palin.
Then again, maybe Hillary would have been the nominee in 2008 or '12 and been elected president, because Captain McCain and Sergeant Hagel had screwed up the war so badly and the country was fed up? Who knows what scandal, misjudgement, or bad turn might have prevented four consecutive Republican White House victories between 2004 and 2016? Certainly something would have. Presidential politics is wildly unpredictable, as someone once said.
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