I have a feeling (though no factual information) that our navy is prepared to shoot down any missiles from North Korea in their (slow) launch stage, when an intercept is relatively easy, and that the North Koreans (and the Chinese) have privately been told this.
Such an intercept was not possible during the Cold War, due to the large land mass of the USSR, but no part of Korea is more than 50 miles or so from an ocean, so I think the N Koreans (and the Chinese, who could certainly stop them) would be foolish to proceed. I think they will back down, much as the Soviets backed down during the Cuban missile crisis.
Maybe Rooster has a more expert opinion on this.