Let’s assume it really was just Trump and a few toadies making direct quid-pro-quos with Russian criminals / officials and that they were so sloppy that it all comes out very rapidly, but also so completely that we can be fairly sure that Pence and the broader GOP had no part in it.
I think in a bygone era, you’d maybe see the Republicans forming a sort of bipartisan centrist coalition government out of fear that everyone would see them reaping the rewards of the crime, even if they weren’t directly involved. That would have been relatively easy at some times, since partisanship wasn’t ideologically-oriented. But now… the party (and their coalitions) cannot be separated from policy. Any change to the status quo on just about every issue is moving the football toward one of the party’s major coalitions’ end-zone.
Best case scenario, Trump makes such a mess going down that Republicans are paralyzed by it, scramble in all directions and just pass continuing resolutions until the next election. But some things can’t be undone, like the Supreme Court. It ultimately comes down to a subsequent election.
If the electorate is sufficiently pissed about the long-term partisan unfairness and empower Democrats with sweeping majorities, and there is a national mood to remove all stains of Trumpism, then maybe they impeach Pence and whoever is in the VP slot (a large enough majority can make any infraction impeachable) and Nancy Pelosi becomes the 47th president in early 2018. And with large and angry enough majorities, the Democrats could increase the number of justices on the court to eleven or even thirteen to essentially nullify Trump’s appointment(s), since the number is determined by statute. And along with that, aggressive changes to election law and voting rights to push back against generations of marginal Republican tinkering that has left Democrats at an electoral disadvantage.
And you could imagine that happening relatively quickly if people are sufficiently angry about what has just happened. Much of the election reforms could be couched in terms to prevent another event like 2016 (and they could make some hay out of the fact that the two most recent historically bad Presidents both lost the popular vote and only won through dodgy external intervention). “The Party of the People”, who first and foremost care about lower-case D democratic principles, and then crucially pass a series of populist, popular reforms that drastically improve people’s lives in concrete and immediate ways, so that they remain in power nationally long enough to keep the pendulum from swinging back.
More likely (assuming it’s not the end of the Republic as we know it), the GOP takes a hit for a few years, “reinvents itself”, and comes back swinging in 2 years. Based on 2006 and 2008, the party of George W. Bush had no business being back in power so quickly, yet here we are.
Edit: That was a lot longer than I meant it to be, but it’s a really open question that (as you said) hasn’t really been given a lot of consideration.
