The US Senate was intended to play that role, but it became a partisan body.
So the US needs something new. Doesn't need to be a hereditary monarchy. But plainly it isn't the Supreme Court, which wants not to be political.
England argued for an English curia, following Magna Carta. The curia was to impose restraints on the king, the primary form of restraint being the law. For king, substitute president in the American conversation.
"That law speaks thus : ‘By me kings reign, by me is justice shewn to those who make laws.’"
... and ...
"The king has a superior, namely, God. Also the law by which he was made king. Also his curia, namely, the earls and barons, because if he is without a bridle, that is without law, they ought to put the bridle on him."
This is the difference between organic development, and theory. We had several civil wars over several centuries to create a form of restraint. During those centuries, we converted the country from an absolute monarchy into a parliamentary democracy with a constitutional monarchy. The US is confronting fundamental flaws in its constitutional architecture.
The US must ravel its unravelling constitution. But to do so, it will need to recognise the problem. Hopefully, it will resolve it without violence.