First of all, I don’t think anybody on the federal level is trying to restrict guns beyond so-called assault weapons, the title of the post, I humbly believe, is a little misleading.
But for the sake of argument, there is only so much authority that the executive office can exercise to restrict weapons access. The Supreme Court has ruled that outright prohibitions on handguns (Chicago and Washington, DC, cities that ironically have high rates of gun crimes) are unconstitutional, so there are limits to how far you can go with banning weapons.
Beyond that, as someone who carries a firearm, I pay close attention to two trends: the first is that these mass shootings always seem to take place in weapons-free zones (Columbine, Virginia Tech, Ft. Hood, Colorado movie theater shooting, and Sandy Hook shootings), which as far as I’m concerned prove that weapoms-free zones do nothing to protect people from criminals or psychopaths who by nature ignore the law, at best, and at worst have blood on their hands because they made people defenseless when these kinds of things happen. These people may be mentally ill or just plain criminals, but they aren’t stupid: they go shoot up places where they know that they will be the only ones armed. Think about that when you go to your local college or elementary school classroom, where you think (hope, really) that no one else has a gun.
The second trend is that when something like this happens, it usually takes someone showing up (with a gun) to put a stop to a shooting in progress. Usually, its the police, but there is precident for armed private citizens having stopped robberies and mass murders in progress. Proof that the best defense against an armed criminal is an armed citizen, generally speaking.