For now, the Electoral College is the way this country elects presidents.
There are some efforts (mainly the National Popular Vote Interstate Compact) to try and move to a national popular vote, but those have so far been unsuccessful.
So what might get us to move away from the Electoral College? A major third party candidate with a base of support in the House of Representatives could do it.
Right now, Republicans feel they have an advantage in the Electoral College relative to the popular vote. (See the 2000 and 2016 elections.) Most Republicans are against any efforts to move toward the popular vote.
A lot of Republicans were for it, however, after the 1968 election.
In that campaign, independent George Wallace won some states and could have prevented either candidate from getting 270 electoral votes. That would have thrown the election into the House. Wallace ultimately didn’t get enough votes, but he came close. He would have had some real bargaining power given you need a majority of state delegations to win in the House.
While the effort to move to a popular vote following that election failed in the Senate, it actually got the necessary supermajority in the House of Representatives to become a constitutional amendment.