How Paul Ryan Saves the United States by becoming President:

Step 1: convince at least 21 Republican Electors to vote for Paul Ryan - look, not every Republican Elector likes the current situation.
That way Trump gets less than 270 votes (he is at 290 now). This HUGE step means President-elect Trump does not have an Absolute Majority in the Electoral College

That event means the House of Representatives must decide the election. The Constitution states the House chooses from the top 5 candidates. With Trump: 269 or fewer, Hilary: 228, Ryan: 21+ these are real possibilities. This has happened before, look it up.:Wikipedia, etc.

Step 2: convince the House to elect President Ryan
At this point it makes as much sense to elect Paul as another option. Trump is a disaster, the House won't vote for Hilary, Paul Ryan is already third in line (and a previous Vice Presidential candidate - which would be Second) so Paul Ryan seems the best choice!

That is it!

p.s. Would you believe I am a Progressive Democrat from Washington State? Yes I am.