We have been through first strike contingencies for over 50 years.
There are no surprises when nukes are launched. We have nukes at the ready in silos, subs and in the air
To be perfectly honest with ourselves. If the US has 10 nuclear warheads that the world knows we can target without fail........Nobody is going to attack us
A country like Russia or China could absorb 10 nukes with disruption, but not collapse. China especially.
With dense population centers, China is most vulnerable. Hundreds of million killed
Their economy would collapse
Back in the 70's I knew some folks that worked on determining minimal capacity to achieve MAD. (At the time I was working on Soviet population figures which they were using). The reasoning goes something like this. First you determine what level of damage an opponent would be willing to sustain. You don't need to kill everyone, you just need to exceed the level that they believe the leadership could survive and and have some sort of country to run. This translated to an eventual casualty figure of about 50% of population (today it would be lower due to better targeting, etc). A case could be made for much lower figures if leaders felt that certain systems such as power generation or transportation were crucial and were both vulnerable and very centralized.
In the mid-70's this level of response gave a figure of about 50 surviving warheads delivered for the Soviet Union. Working backward, they then tried to compute how many warheads and delivery systems were necessary to "assure" the 50 strikes. It worked out to about 250--350 warheads. Finally, you had to factor this up by 20% or so to account for the fact that not every warhead is on line at all times (subs and planes can be in the process of maintenance and ICBM's are not continuously fully fueled). So you end up with 275--420.
Now, I would imagine that other factors are of more concern than determining this force level to achieve MAD, like the problems of identifying the origin of an anomalous single strike. We are far more likely to need to respond to a radiological weapon used by a non-state entity than a full-blown nuclear strike. This makes accounting for all the weapons-grade nuclear material sloshing around the world a very high priority which receives very little press coverage.
IMHO the doctrine of MAD is outdated in a world where the biggest risks are from players who believe they will not be identified or who believe that they have no society to protect from nuclear retaliation (i.e. they are embedded in a larger society which we could not effectively separate from the bad players). To the extent that it is still useful, we probably could be just as safe with 500 warheads as with any larger number. That number could be slashed much further if we have made advances insuring a larger survival rate of warheads, which I speculate is the case.
The argument for reduced stockpiles is that in a variety of ways maintaining them is incredibly expensive. The fissile material needs to guarded for centuries after decommissioning, far outweighing the considerable costs of producing and operating the weapons systems during their lifetimes. We know how to destroy biological and most chemical weapons, but not radiological risks.
I'm not trying to argue numbers here, I just want to lay out the reasoning behind getting to a number, especially the crucial role of determining the survival rate of delivery systems. I assume that the other major nuclear powers do the same calculations on the USA. If you think a higher number is warranted, at what stage of the process do you think the calculations above are off?