Trump has invited all 100 senators to the White House for a classified briefing on the NORK situation. That's some kind of a first. I never heard of that happening before.
The NORKs have threatened to sink the USS Carl Vincent. And to nuke the US mainland. As for the carrier, they could get lucky with a diesel-electric sub, of which they have some. They would have to be pretty lucky to avoid detection and destruction by the carrier's escort destroyers, and they would have to get several torpedo hits, but it might happen. If they actually sank the carrier, as opposed to just launching on it, they could expect retaliation, probably air strikes. If the NORKs have a working nuclear warhead for a missile, that they have never tested, they might be able to nuke the western US. That ought to buy them wall to wall airstrikes, with nukes.
Going up against the NORKs with ground forces amounts to starting up the Korean War all over again. The NORKs have strengthened their army since the 1950s. The South Koreans have a large army, probably more motivated, better trained, and better equipped, but probably not enough to bring a quick and easy victory.
Our best bet is to convince the Chinese to cut off the NORKs imports of food and fuel. The Chinese may or may not go along with this. They want to keep the NORKs around for all the grief they can give the Americans and the South Koreans. And to keep a unified Korean, which would be run by the South Koreans, off their border.
If the Chinese option doesn't work (pretty likely) then the only other option I can see amounts to assassinating Kim Jong whats-his-face. That would bring the regime down in a welter of back biting and attempts to seize power. This might be our best option if we want to put the NORKs out of the nuclear business. The current NORK regime is dead set on getting nukes and the missiles to launch them. We will need to do regime change on North Korea to change that.