Let's talk about the effectiveness of a ban. I'm going to have to assume that somehow such a law would get passed by Congress, which in-and-of-itself would require a paradigm shift in American politics. But, let's say that it happened.
America has 65% more guns per capita than the next highest country. We have almost twice as many as the next highest first-world country (anyone want to guess who it is? Switzerland!).
I don't know how many guns GB had when they instituted their laws, or Australia or any other country like that, but it's a safe bet that, given the high incidence of firearms in the us, that it would take far longer for them to "die out".
However, I did a little research into GB gun laws. Turns out, anyone can own a rifle or shotgun so long as they have a legitimate reason to do so. Hunting and sporting are legitimate reasons. So, if such a law were enacted in the US, all someone would have to do is say they were using it for target practice (perhaps join a club) or that they go hunting, and they could legally own a rifle or shotgun.
But, handguns (less than 30cm/11.8" barrel) are generally prohibited. Given that handguns make up almost 73% of all gun-related homicides, handguns should be the focus of any legislation.
I simply don't see how you get people's handguns.