There have been various discussions recently regarding whether it might be possible to find a loophole so that a candidate could run for a third term as US President without violating the Constitution. But setting that question to the side for the moment - who is responsible for enforcing term limits in the first place?
In other words, suppose a president just brazenly ran for a third term, without making any attempt to hide the fact that he was violating the Constitution. How would this be stopped? Does his party have a legal duty not to nominate him? Does the electoral college have a duty to overrule the election? Does the Supreme Court have a duty to disqualify the candidate? Is the whole thing just on the honor system??