As far as I know, with existing known technology and defenses, there's probably a number n, such that if you launch more than n simultaneous non-hypersonic cruise missiles, an aircraft carrier is going to be unable to deal with them all. This of course assumes you can launch that many missiles, in range of the carrier, simultaneously, without advanced warning.
Now, the navy also isn't dumb, so I'd venture to guess they avoid parking their carriers within that range when possible, and that they probably have some other defenses like C-130's and other ships mounted with directed energy weapons and other missile defense and whatnot. I imagine they also aggressively pursue and maintain intelligence on the location, number, and readiness state of those missiles. This starts to get complicated because there's a complicated interplay of strategy and tactics related to the off-ship capabilities, and defenses have counter-strategies (such as launching a bunch of Surface-to-air missiles at those C-130's immediately prior to launching the cruise missles) and those counter-strategies have counter-strategies, etc. etc.
I also have no idea what that number n is. It could be infeasibly high.