Nor does the Unha-3 missile, which Pyongyang used to launch a satellite in December, have the guidance systems and re-entry technology necessary to deliver such a nuclear weapon onto an American target - which would have to be in western Alaska, since that is the limit of the rocket's range.
There is no doubt that Kim Jong Un's regime is feeling extremely peeved about the international response to its weapon and missile tests, which has included tighter United Nations trade sanctions that got unanimous support in the Security Council. Even North Korea's only ally, China, voted for them.
In a fit of peevishness, he [Kim Jong
Un] has even cut the military hotline between the two sides at Panmunjom. But it's really just an empty gesture: an alternative military communications line, used to monitor cross-border workers at the Kaesong Industrial Complex, remains open.
But it's a long way from feeling peeved to feeling suicidal.
Any North Korean nuclear attack on an American target would be answered by immediate US strikes that would annihilate the military and civilian leadership in Pyongyang, obliterate its nuclear facilities, and probably destroy much else besides.
So North Korea's threat to launch a "pre-emptive" nuclear strike against the United States, or even against South Korea, is totally implausible.
However, the young and inexperienced North Korean leader may feel the need to prove his mettle to his own military commanders by taking some more limited action against the US-South Korean exercises. That sort of thing can easily go wrong.
There is a widespread perception in South Korea that Seoul was caught off-guard by North Korea's sinking of the warship Cheonan and its artillery attacks on Yeonpyeong Island in 2010. North Korea paid no military price for either action, and South Korea's newly elected president, Park Geun-hye, who took office only two weeks ago, needs to show South Koreans that she is not going to let that happen again.
She probably also hopes that a promise of prompt and severe retaliation will deter North Korea from any future attacks of that sort.
So she has engaged in some rhetorical escalation of her own.
She has warned North Korea that any further attacks will be met by instant retaliation that targets not only the units involved in the attack, but also North Korea's high command.
No doubt this is only intended to deter any such North Korean attack, but in practice it means there will be much more rapid and uncontrollable escalation if Pyongyang makes a token attack anyway.
Even a conventional war in the Korean peninsula would be hugely destructive. Just north of the "Demilitarised Zone" between the two countries is the largest concentration of artillery in the world, and the mega-city of Seoul is within long artillery range of the border.
North Korea's population is considerably smaller than South Korea's, but the North maintains the fourth largest army in the world. Its armed forces operate mostly last-generation weaponry, but the equipment is well maintained and the soldiers appear to be well trained. The last war between the two countries killed over a million people and left all the peninsula's cities in ruins - and that was over 60 years ago.
If North Korea ignored Park's warning and made some local attack to demonstrate its displeasure, and Park then felt obliged to act on her threat to go after the North Korean leadership in Pyongyang in retaliation, things could get very ugly very fast.
So far the US-South Korean exercises have gone off smoothly but the risk of a serious miscalculation first in Pyongyang and then in Seoul is real, and the exercises still have more than a week to run.