is it unconstitutional to prohibit citizens to have nuclear weapons?

[Peter]

Don't be utterly ridiculous.

To exercise any of its enumerated powers the federal government has to be able to guarantee that it, you know, exists.

Given that civilian ownership of nuclear weapons could well spell the end of the federal government (not to mention a hell of a lot of people), I would say that the federal government can use the elastic clause to ban civilian ownership of nukes so that it can actually exercise its enumerated powers.

[Peter]

To exercise any of its enumerated powers the federal government has to be able to guarantee that it, you know, exists.

You shouldn't assume that they want the United States government to exist at all.  It is just a barrier between them and the anarchy that they desire.

They might not wish it to, but I somehow suspect that the Constitution does.

[Peter]

An armed populace is a check on the government itself, to ensure that the government is actually doing its job - it is only a threat to the existence of tyranny, not a republican government. One crazed fanatic alone with an assualt rifle in this armed populace does not in of itself present a threat to the existence of the federal government.

However, if this crazed fanatic gets a hold of a few nuclear weapons, we move into a different ball park - he is then able to actually threaten the very existence of the republican federal government, and therefore stop the federal government from executing its enumerated powers. Obviously the elastic clause can and should be used in this circumstance to ensure the continued execution of the enumerated powers.

[Peter]

The "common defense" clause is an authorisation to spend money for the common defense, it does not allow for regulation in the interests of the common defense. This does not mean that Congress cannot regulate the entities it creates for the common defense however, as this is authorised under other clauses.