Well, the U.S. experience with them is that they have gone to state ballots -- and some of our states are larger than some European countries.
These ballot measures usually get voted down, as happened in California (some sort of handgun restrictions) and Washington state (licensing/registration of handgun owners and all transfers, failed 71%-29%). Every now and then, a limited one gets passed, as happened in Oregon and (IIRC) Colorado for the so-called "gun show loophole" background checks.
The media doesn't like to mention the times when gun control lost at the ballot box. They'd rather hype the times when it passed, so that they can make it look popular.
As far as federal, there is no provision for that in U.S. law, which is why it won't happen here. And the feds seem to want to keep the fiction that the 2nd Amendment doesn't apply to the states. . . .