Interesting theory that people would demand doomsday for some ships getting sunk. That people cannot accept the end of their empire's military projection. The US should then preemptively use nukes, with popular support, in any war they will fail in. Guarantee you that there will be no referendum on retaliation, only the usual media militantism and tyranny.

The MAD doctrine only gets invoked at the sight of several incoming missiles on territory. It is your response to navy being sunk that causes MAD.

And every major population in the U.S. would be annihilated in return. If China decided to nuke their own coast, America would either do nothing about it or come to a swift and total end.