Of course it is possible to get 50% of the vote and lose the election (see 2000) -- but not likely.
Dear liberal hack,
Al Gore got 48.4% of the vote.
And George W. Bush got less, but still won the Presidency. That is the point.
Al Gore got slightly more than 50% of the votes cast for the candidates of the two main parties.
So how is it possible to win 50%+ of the popular vote and lose in the general election? It's simple: one wins by tiny margins in most of the states that one wins, and loses by huge margins in states that one does lose. Winning Texas by 30% means just the same as winning Texas by 2%; one still gets Texas' 38 electoral votes. Winning California by 2% means the same as winning California by 30%; one gets its 55 electoral votes. Winning Georgia by 20% has the same effect as winning the state by 2%; one wins the 16 electoral votes of Georgia.
Work the model out in which those are the only three states. No matter how badly a nominee does in Georgia and Texas, even a bare win in California wins the Presidency by a margin of 55-54. That is of course a horrible system, one that likely breaks as Georgia and Texas secede.
I didn't realize that's how you count votes. "Third parties don't matter, so count them out." What else? Do we unskew votes for how Republicans keep people from voting in states?