I'm not aware of any real factual support for this sweeping claim. The dreaded "assault weapon" is merely a semi auto rifle. You could ban them I suppose, and make criminals out of millions of law-abiding hunters and recreational shooters. But then logically you would also have to ban semi-auto shotguns and pistols. Let's be honest here, that is exactly what the anti-gun crowd want to do. They just are not honest enough to come out and say it.
The vast majority of mass murders in the US are made possible by the use off semi-automatic weapons. Remove them or do something, anything such as regulate who can obtain them and it is almost certain less people will die.
The anti-gun crowd just want to see a few thousand less people being slaughtered every year. That simple really.
I'm not American but if I was, I would have supported the anti-gun movement the minute I was old enough to understand that one mass shooting is one too many and guns should be removed entirely, or at least from sight or reach of untrained hands and unsteady minds.