It would work...for about 3 days.
Right about that point, all the nuclear powers in the world (except Israel and the UK) would wonder if THEY were next on the list...and launch everything they have at us.
There would be NOTHING left, anywhere.
A better idea would be: get Riyahd, Tehran, Damascus, Amman, and Cairo. Drop 5 each on Mecca & Medina. Notify Israel they can do what they want to the Dome of the Rock.
The NCA (whoever it is) would get on a worldwide broadcast and say that unless the living bodies (or the whole dead ones)of all known terrorists are not on planes headed for whatever city they designate within 24 hours, 5 more cities with major Muslim populations would be destroyed.
If they find out the bomb came from China, demand the resignation of the entire Chinese Politburo and the handing over of the government to the US ambassador, OR kiss Shanghai goodbye, and one Chinese city a day until it happens. Same thing applies if it's a Russian bomb...and with the Russians, notify them that if they attempt or even LOOK like attempting a launch against us, it's no-holds barred.
Inform the world that the US has just become the Absolute Power, and someone just crossed the line. One move out of place, and you no longer exist.
Sensible enough to me.
Alas, the puppet masters have other plans.