To the OP's question, here is the way I see it as a socialist:
The Second amendment doesn't mention firearms at all, it mentions arms, which could be anything from slings to rocket launchers. This means that any weapons at all not allowed is a limit on the second amendment, and since this is a limited right, I don't see anything unconstitutional about these limits. Assault weapon bans, or even outright bans on guns should technically be constitutional by the letter of the law at the very least, so long as some arms are still legal.
That being said, I disagree with firearm bans basically always, not because of the constitution but because I generally feel that freedom is best served by things that are regulated and available. I wouldn't be opposed to universal background checks, mandatory safety training or even licenses in order to use a gun (you need one for a car, and it isn't even designed to kill anyone). I don't see the issue as something particular to firearms, I believe basically there should be few limits on what is allowed provided the regulations are tight enough.
The biggest thing that confuses me about the issue though, is why is it so important? What makes a gun special versus any other weapon? Don't misunderstand, I do have a m1911 and I generally feel people have a right to self defense, and since I am technically in VA (Rather than DC or MD) I can use a concealed carry permit and other such things, and I don't oppose them. The thing is owning a gun hasn't changed my life in any appreciable way, I still don't walk around with a gun everywhere, even if there were an outright ban how would it even effect me, and don't say I couldn't rebel against the government, because that isn't going to happen gun or not, I am not the sort to engage in a violent struggle, especially one I would be destined to lose. Perhaps this is some sort of cultural difference between the right and the left, but I can't imagine life being all that different with or without private ownership of firearms.