As far as the Constitution is concerned, no one votes for President on Election Day, rather the State Legislatures have chosen to allow them to vote for Electors. If for some strange reason, all 538 Electors nominate different people, then it would be a wide open race in the Congress with the House having 538 choices for President and the Senate having 538 choices for Vice President.
Isn't it limited to only the top three?
Yes... but if 538 people tie for first slot...
Of course, in theory electors do not have to cast a valid vote (also, what are state procedures if noone wants to be an elector?) so it could still theoretically happen.
And no, the Constitution does not address such fancy issues. Very little of actual US constitutional law and custom is actually Constitutional text.