Then it goes to the house where the states get a single vote (each rep votes in their state caucus.)
Still tied? It goes to the senate.
Still tied? I decide. I select myself.
So, yeah. You don’t want that to happen.
The Senate has no role in the selection of the president, only the vice president. Jefferson was selected in 1800 after 35 ballots in the House which could not defeat Burr. Only after Hamilton persuaded a Federalist not to vote on the 36th ballot did Jefferson become president. This was one of the reasons Burr killed Hamilton. Hamilton considered him another Cataline while Jefferson had “pretensions of integrity.”