If making gun possession illegal in the states would guarantee that criminals didn't have access to guns, then I'd say: Screw the constitution, make guns illegal.
Unfortunately that's not how it works. Making guns illegal just ensures that only criminals have guns.
Even if all gun manufacture is halted in the states, and it's completely illegal to even bring a firearm into the country. Criminals will still import guns illegally.
What it WOULD accomplish is stopping idiots who THINK they can help by owning a gun, from being stupid and shooting innocent people on accident.