John Kasich, the governor of Ohio, as the 45th President of the United States? It could happen.
Here's the situation. Some Democratic electors and Republican electors who are fearful of Donald Trump and don't want him to become President want to reverse Trump's 306-electoral-vote majority. One Texas Republican elector has already whittled away at Trump's majority, saying he will vote for someone else, so he cut it down to 305 (couldn't resist the Billy Joel reference). Democratic electors, knowing Republican electors will never vote for Hillary Clinton, are trying to get enough Democratic and Republican electors - 37 in all - to vote for a compromise Republican presidential candidate and deny the Donald a bare majority of 270 votes. If no presidential candidate gets an electoral majority, the House of Representatives chooses among the top three vote-getters, with each state having one vote. With the House under Republican control, the hope is for 26 states to vote for the compromise candidate and make him President. Kasich is the likeliest compromise candidate in this scenario.
Kasich is no great shakes either - he stopped high-speed rail in Ohio and went after Planned Parenthood - but many people think he'd be a safer choice for President than Trump.
So we'll see. This should be interesting with regard to the transition from the outgoing administration, as the electors don't vote until December 19 and their ballots aren't counted before a joint session of Congress until January 6 - two weeks before Inauguration Day. How would President-elect Kasich or whoever President-elect Not Trump would prepare for a new administration in what our British cousins would call a fortnight? But the prospect of stopping Trump in the Electoral College is still a long shot.
(Note: Mike Pence would still be elected Vice President by the Electoral College. Were no vice presidential candidate to get a majority, the Senate would choose between the top two vote-getters, with each individual Senator having one vote. That happened only once, in 1836.)