'Accepting' a Nuclear North Korea?

Via the BBC:

The US will not accept a North Korea armed with nuclear weapons, a top US envoy has said, after Pyongyang announced plans for a nuclear test.

To which Kim Jong Il said, "Pffft! What are going to do about it? You're bogged down in two wars against countries without militaries. I have a 1.08 million man army!

North Korea must choose either to have a future or to have nuclear weapons "but it cannot have them both", top US negotiator Christopher Hill said.

He did not specify how the US would respond if a nuclear test took place.

Now, correct me if I'm wrong, but isn't it correct that out of the three members of the 'Axis of Evil' two are currently nuclear power and the one remaining nation in the 'Axis of Evil' happens to be the one where our military is bogged down, bleeding itself dry, preventing us from being able to address the nuclear threats posed by the other two?

I'm not an expert strategist, but it seems to me that if you're planning to 'start with the small threats' and then to 'work your way up' it's best not to choose a 'small threat' that will keep the bulk of your deployable military assets tied up for a decade for the first strike.

Oh, and once you are bogged down, all the blustering and threatening won't get you unstuck. It won't convince anyone to stop doing anything either...

North Korea Axis of Evil Nuclear Proliferation Quagmire