Odds are low, but there are plausible scenarios in which the election ends in a tie, 269 to 269. In such as case the House of Representatives chooses the President (from among the top 3), and the Senate chooses the V.P. (from among the top 2).
It happened before (with slightly different rules), with Jefferson and Burr finishing in a tie. The House took 36 votes over eleven day to choose Jefferson. On the first 35 votes, eight state delegates voted for Jefferson (when he needed nine states), six for Burr, and two were tied. Jefferson needed nine for election. On the 36th votes, upon the advise of Alexander Hamilton, several Congressmen changed their vote, and Jefferson was elected with the support of ten states.
The nation survived, although Hamilton did not.
https://www.youtube.com/watch?v=LnHVFAm0TTk
The 1824 election also went to the House of Representatives because no candidate had a majority.