What do you think would happen if Hillary won the presidency by the electoral vote while Trump won the popular vote?
First, it would mean Hillary had really bad turnout problems, likely resulting in Congress remaining Republican. Second, the popular perception and opinion would probably be severely against Clinton, leading to similar "not my president" and such demonstrations.
I think most of all, though, is that there would be a sustained movement to eliminate or severely alter the electoral college (I'd guess to one based on congressional districts rather than straight up national popular vote, since a popular vote one is unlikely to get the support of the flyover states). I don't think it would take very much to switch the tea party folks to going from Obamacare to the electoral college.
I haven't really seen much from the left-leaning side about altering the electoral college since Trump was sworn in. Everything's now been focused on him and his "outrageous" policies. That very well could have also happened in the reverse--but if Congress was still Republican, I'm not sure if the protests would all be focused on her. Congress could block her while the people would be free to fume over the electoral college and demand reform.
That being said, I still don't think even mass outrage from the Republican areas would cause an amendment to fully pass. State legislatures know full well what a popular vote (or even congressional district) election would mean to their state's importance in the election and even with a lot of angry constituents, I doubt that'd be enough to sway them to cut off their own nose.
What's also not being taken into consideration is the National Popular Vote Interstate Compact. If Trump had won the popular vote, then come December 19th, the electors from California, Washington, Illinois, D.C., Maryland, Massachusetts, New York, New Jersey, Rhode Island, Vermont, and Hawaii would be in a pretty bad spot--either back the compact and popular vote or prove the whole thing's a sham since it would elect the "wrong" candidate.
…closest in recent U.S. history…
Depending on how you define "recent," the attempt in 1970 is the closest so far. It had Nixon's support and passed 339-70 in the House before failing in the Senate 54-36 (technically, the Senate never actually voted it down, only filibustering the bill until the end of the term). 30 states were likely to approve it, 6 were leaning toward, 6 leaning against, and 8 firmly opposed (38 are needed).
