True assault weapons - that is, weapons capable of automatic or burst fire - are already illegal to civilians except those with a very restrictive permit. To my knowledge no one, not even the NRA, opposes this.
And yet, does anyone remember the LA bank robbery in 1997? The one where the robbers had automatic weapons, drum magazines, armor piercing rounds, and body armor? Laws restricting Automatic weapons, high-capacity drum magazines, and felons from buying weapons didn't help much there.