Now there is a problem with this.
What happens when no one wins the overwhelming majority?
Well, we already know the answer, because this has already happened before.
In the election of 1824 there were four major presidential candidates, all of whom won electoral votes.
Now, Andrew Jackson actually won the most electoral votes, but he didn't have the overwhelming majority of the electoral votes. Due to our laws the election was resolved this the United States Congress. The House of Representatives voted on who would become President (mind you they only got one vote per state, rather then one vote per Representative), and the Senate voted on who would become Vice President (in this case each Senator gets one vote).
In the end John Quincy Adams was elected by the House of Representative to become the President, while John C. Calhoun was vote in by the Senate to become the Vice President.
So back to the question at hand, is it still possible that only two candidates who win all of the electoral votes between that neither one of them still not win the election?
Yes, it is possible.
As you can clearly see the electoral votes are even, and if a candidate was to win the ten states with the highest number electoral votes plus either Virginia, or any combination of states that make up 13 electoral votes, then that candidate will have only 269 electoral vote (as will the other candidate).
Of course this combination isn't actually need, this is just the fastest one I came up with. There are probably dozens of different combinations that can cause this. Plus there is what is called a Faithless Elector who chooses to vote for the candidate other then the one that the other Electors in that state have pledged to vote for (or not vote for anyone if they choose to) and thus you end up getting a tie that way, or neither candidates having enough votes that way.
Then there is of course the possibility of a third candidate (or more) capturing enough electoral votes that it causes the two top candidates to not get enough electoral votes to win.
So in theory it is possible for two major candidates to get a tie in an election (or neither get enough electoral votes) and so what would happen is that for the second time in our history is that our Congress would choose who would become President and Vice President of the United States.
Scary thought, isn't it?
The current Electoral Map of the United States