The Republicans' game -- down the Constitutional rabbit hole
Even to guys like Ryan and McConnell, it must be obvious that a Trump Presidency would be intolerably dangerous. He's not even in office yet and he's already created an international incident with China, he's blatantly kowtowing to Russia, he refuses to take intelligence briefings, and in general he's randomly blundering in ways which, continued over four years with the full power of the Presidency, would inevitably mean disaster. He's also blithely tossed a number of right-wing sacred cows in the dump, such as free trade. Even if he doesn't cause a nuclear war or a global economic crash, he's likely to mess up badly enough to provoke a huge anti-Republican backlash in 2018 and 2020. Party leaders understand things like this.
That doesn't mean, of course, that they want to respect the popular vote and make Hillary President by a revolt in the Electoral College. They want a Republican -- just not Trump.
What I think they're doing is allowing a case to be built for impeaching Trump as soon as possible after he takes office. Collaboration with a foreign power to subvert the election would certainly qualify as grounds for doing so. If Trump becomes President and is then removed, Mike "God hates fags" Pence becomes President. And most Republicans would be totally fine with that.
By the way, about that Electoral College gambit -- yes, Trump's unprecedented unfitness for office makes it somewhat credible that as many as 37 Republican Electors might defect and deny him an absolute majority, but it's still very unlikely that 37 Republican Electors would defect to Hillary. Defectors would be far more likely to choose some other Republican -- Romney and Kasich have been mentioned as possibilities. If no one gets an absolute majority, the choice moves to the House, where a majority of state delegations are Republican-dominated (remember, if the House chooses the President, it's one vote per state delegation, not one vote per member). Republicans would probably split, since many don't want Trump but also don't want the onus of installing the other Republican who got none of the popular vote because he wasn't even in the election. Assuming the Democratic delegations voted for Hillary, no candidate would get a majority.
Now get out your Constitution and turn to the Twelfth Amendment, and also section 3 of the Twentieth Amendment, which supersedes part of the Twelfth. If the deadlock in the House continues through January 20, the Vice-President-elect becomes acting President until the House gets its act together. And the Vice-President-elect would probably be Pence, since in this scenario the Senate would have chosen the Vice-President, and the Senate has a Republican majority. (If you want to speculate that three Senate Republicans could be persuaded to defect and choose Tim Kaine as Vice President, go right ahead, but then I suspect the House Republicans would unite behind the non-Trump Republican option the Electoral College had given them, popular vote be damned.) Assuming the House never did settle on a majority for one candidate, Pence would simply continue in office.
One final oddity presented by this scenario is that if the Democrats somehow won a majority of House state delegations in 2018, they could elect Hillary as President on the grounds that Pence had merely been the acting President for the past two years, pending a House majority for a single candidate. Whether they could actually make that stick, probably only a true Constitutional scholar could figure out.
So our best-case scenario here is to get one of the most theocratic and homophobic politicians in the US as President, even though Hillary won the actual vote by a margin approaching three million. For the future, our country can avoid a recurrence of this bizarre mess by enacting the National Popular vote initiative. If you live in one of the 12 states where it has been partially enacted or in one of the 27 where it has not been voted on yet, consider contacting your state legislators and urging them to support it.
Update: If there is indeed a Republican plan to use the Russian connection to take Trump down, Fox News seems to be on board with it.
[Image at top: The likely President for most of the 2017-2020 term, caption by Mock Paper Scissors]