Protected, as I said, by the second amendment. I suspect, however, that an aircraft carrier (even without the air wing, much less the battle group) is more expensive in real terms than any American privately owned armed vessel was in the late 18th/early 19th Centuries. Probably more expensive than a Ship of the Line was.
Looking at warship price as a percentage of GDP, the HMS Victory was 0.07% of Britain's GDP at the time, while 1980's British carrier HMS Invincible was 0.08% of Brit GDP at the time of launch.