Even if the insane regime in Pyongyang were to run their puny atomic production facilities 24 hours a day, 7 days a week for the next 10 years, they would have but a fraction of the nuclear firepower in just ONE Ohio-class SSBN, which as a matter of fact could target the entire North Korean nation while casually docked in Hawaii.
At some point, the ChiComs in Bejing are going to realize that if the North Koreans provoke a nuclear exchange with the U.S., that fallout recognizes no national boundaries. It will then be in their best interest to give Kim Jong Il and his crew a sendoff worthy of Ceausescu and his wife in Romania.
Every bit as much as that, I doubt very much that the PRC wants a democratic 'south' Korea right on their border- which would be the logical outcome of such a war. Last time that almost happened, the Chinese responded militarily.
The North might have a chance if they keep their strategic weapons holstered and go conventional. Maybe.
Would that be the ONE in the East China Sea, or the One in the Sea of Japan? :)
Seriously though, I don't think there are enough targets in North Korea to be worth dedicating a single Ohio to them. Just a couple of LA class attack subs with nuclear armed Tomahawks, or maybe a couple of Frigates similarly armed.