It depends on what you mean by 'destroying it's enemies many times over'.
For example the USSR had about 1400 ICBM silos and given the likely reliability of US nuclear missiles each silo would need 2 or 3 warheads. So that alone is about 4000 warheads of the power and accuracy that can crack open a silo designed to withstand 2000psi overpressure.
Then there are the airfields on which long range nuclear aircraft are based, dozens if we are only counting intercontinental bombers but hundreds if we get down to Tu16s and Su22s both of which are a theatre threat. Again these aircraft are protected and their weapons are in hardened bunkers so these airfields will need multiple warheads, so maybe another 1000 warheads.
Then there are the naval bases where ships and subs with nuclear weapons are based, there would be maybe a dozen or more which will also require multiple warheads, big ones for these 'area' targets, so there's another 100 megaton warheads.
Nuclear weapons require a considerable amount if servicing, to replace decaying tritium and the like. So with a bunch of warheads in these repair/service pipelines these facilities will have to be hit, as well as nuclear warhead production facilities, so hundreds more warheads are required.
So before we even get into the limited war bullshit the US needs maybe 5000 warheads just to cover the basic most threatening targets in the Soviet Union. If we bring in other possible targets and broader contingencies the requirement goes up and up and up.
Sigh!
