"If the U.S. keeps pestering us and increases pressure, we will regard it as a declaration of war and will take a series of physical corresponding measures,"Given the lack of force projection capabilities possessed by the People's Democratic Republic, it's hard to imagine what these physical measure might be. Holding their breath until they turn blue? Rolling on the floor and pounding on the carpet?
Their realistic options for striking directly at the US (as opposed to launching a general war on the penninsula) are limited, and none posit good outcomes for Kim Jong Il & Co.:
1) Smuggle a nuke into the US, perhaps into a port via container ship. In this scenario, they set off a fifteen kiloton warhead in the harbor of, say, Seattle or LA. In return, they get a fifteen megaton airburst over Pyongyang. It's hard to see what they gain there.
2) A strike on US facilities in Japan or South Korea. This brings additional nations into the war, and creates a remilitarized Japan, something no Asian nation wants to see.
3) Well, numbers one and two are really their only alternatives...
Also, it seems that the Norks are busy finding out the hard way that, if it comes to choosing which is the more important trading partner, Beijing is going to pick Bentonville, Arkansas over Pyongyang any day of the week.