Hans hit the big points, it would be difficult but not impossible for most countries to muster enough effective cruise missiles or bombers to neutralize a US carrier battle group. And even if the OPFOR do manage to humble the Navy there are a half dozen plus carrier groups to help take up the slack. Read Tom Clancy's Red Storm Rising (excellent book) to get a read on how a battle group is tooled against missile threats. I don't think it's changed significantly since that book was written. A sub might be able to get the carrier if it's skipper played his cards well but he would only get one shot.
It isn't impossible though I recall one particular war game back in the early 2000s they ran where one side sunk most of a battle group using little but light patrol boats. The admiral running the war game restarted the scenario and imposed so many restrictions on the OPFOR that the rest of the results were a wash.
I'll agree that against most current cruise missiles with their 500lb HE warheads probably wouldn't be able to sink a battleship without a inordinate number of hits. But it would certainly wreck havok topside which can be just as bad and if they don't already exist building an armor piercing warhead for a cruise missile wouldn't be hard. A shaped charge warhead or a rocket boosted final stage would probably be sufficient to get through the belt. If someone wanted to kill a battleship with missiles it would be a small leap from current weapons.
While rail guns would negate the biggest disadvantage naval guns have vs missiles (range) the armor and slow firing rate per barrel is what let those things grow so huge. With a dozen or two Mega Joule railgun capable of 10RPM (that's what they're trying for) would allow a two barrels to exceed an Iowa's firepower. That's not taking in account the terminal performance of the guns.