The problem with minimums is that the minimum keeps increasing.
In order to deter an attack, there has to be enough firepower, in both number of warheads, and yield to remove the attacking country from the course of history, that is destroy every military installation and every city. This is a pretty horrific thing to contemplate but we have to be able to deter people who do not share our values. A minimum unacceptable loss for us (several cities and other strategic targets flattened, millions of individuals slaughtered) probably won't deter someone who thinks Mao or Stalin were peachy keen fellows who made their countries strong by being willing to sacrifice. Where we see unfathomable, senseless loss of the potential represented by individual people, others see martyrs to rally the survivors around. Thus the minimum to deter a statist autocrat is whatever is required to totally anihalate their means to power...their state, that means all of the infrastructure.
It gets worse.
As more countries get these hideous weapons the minimum number goes up. The arsenal must not only deter an attack, there must be enough warheads to survive a first strike, destroy the offending nation AND enough left over that after such an unGodly cock-up no one will fire their arsenal at us, secure in the knowledge that since we just expended our arsenal in a fit of reciprocity they can take out a competitor on the world stage with minimal retaliation. The possibility of two states combining their arsenal against us can't be dismissed out of hand either. Again we aren't detering against people who think like us...Against, rational, and somewhat risk adverse western polities, the UK, and France have perfectly adequate arsenals. Against totalitarian autocrats, deterrence is a much higher bar. Against the 12ers of Iran deterrence has little if any utility once they get an arsenal of some as yet undetermined size (I'd guess between 30 and 100 weapons, but that's a stab in the dark).
I suspect that the New START limits (1550 warheads) are probably too low, which is understandable given that they are an agreement that does not take into account China. The SORT limits of 2200 would seem to be more realistic. Such an increase might actually appeal to the Russians who put rather more of their military into nukes that we do.