The problem is that too many guns exist already in the USA. If guns had just been invented and only a few of them existed, or if we were a moon colony that had never imported guns, or if we were some country where, due to social/cultural/political circumstances very few people have guns, then gun control would stand a chance of working.
But we have to work with what we've got. The situation we're actually in is this: Even if we could get the massive political coalition it would take to repeal a Constitutional amendment, there are still millions of guns that exist in the USA.
There was an article on HN very recently about a site that allows buyers and sellers of guns to find each other and go through transactions using Tor and Bitcoin for anonymity. So I think it's fair to say that the advancing state of software and Internet technology will make it increasingly easier for people to obtain firearms illegally.
So if you outlaw guns in the USA, the practical effect is disarming responsible, law-abiding citizens, whereas anyone who's bound and determined to get a weapon and doesn't care about the law, can still get one.
(Presently I believe there is a federally mandated waiting period and check for felony records for those buying firearms, called the Brady bill; the idea is to make sure you have time to think about what you're doing and have a few days to "cool off" if you're angry about something.)
My state recently passed a concealed-carry law, whereby any citizen can become certified to carry a concealed weapon. The controversy surrounding that has made me aware of an interesting argument:
What if we go in the opposite direction?
If we assume most people are responsible enough to handle firearms, and a non-negligible percentage of the population carries concealed firearms wherever they go, then it's harder for mass tragedies to occur. When the crazed maniac begins his massacre, the would-be victims can start shooting back.
Concealed carry can also serve as a deterrent to violent crime like armed robbery. If you're desperate enough to try something like that, and you know you're gonna be the only one with a gun, you also realize that the worst thing that will happen is you get three squares a day and a roof over your head at taxpayer expense. Whereas if you know there's a decent chance somebody else will have a weapon, suddenly the worst-case scenario becomes a hole in the head, which might affect your calculations enough to change your decision.
That's the argument, anyway; I'd be interested if anyone can find holes in it.