I doubt any such ban will pass as law. There is simply no support for it. Just like after the last few massacres in the US, there'll be some political to-ing and fro-ing, maybe a committee will be formed, a bill will not be passed, and nothing of any conviction or lasting value will happen. There's no support for gun bans, and there's no money for meaningful mental health reform.
Six months from now we'll be having the same conservation, just relating it to a different mass killing.