nuclear retaliation is a v likely response to a destroyed carrier doctrinally
US has publicly announced that use of nuclear weapons against a CVN would be considered as the same as a nuclear attack on any normal airbase and be subject to the same retaliation

that is well outside their capability tbh, their radars lack both range and resolution to achieve multiple direct hits on the protected center of a battlegroup at standoff range

tbh CVN groups are v testy about neighbors
worst case scenario they can go away from people who are within a few horizon spans at 36 kts

usn officers and admiralty would sooner give up an entire us state than one of their precious carriers. doubly so if its some irrelevant one like iowa or something