It has already happened of course.
I've been an advocate for some while now for adding "has been committed to a mental institute/judged incompetent" to the NICS system.
Of course there's a catch... criminals and crazies don't HAVE to go thru legal dealers or NICS. They can buy off the black market. No matter what laws you pass, the black market will still provide those things people want that are illegal. Just like weed and meth...
So I have grave reservations that expanding background check requirements would actually do any great good in the real world as-it-is, especially given the Fed/ATF's absolutely miserable record on enforcing and prosecuting the EXISTING system of checks (NICS) and those who try to get around it (last I checked, 7 convictions out of 250,000 detected attempts, pitiful).
So yeah, if a proposed gun control law doesn't appear that it would do any ACTUAL good, I'm not likely to support it just because it "looks good".
Bear in mind, when I was 24 my best-friend-like-a-brother was murdered in a robbery at his business... taken off and shot in the head with a .44 magnum. I didn't blame the gun; I blamed the murderer.
And I also blamed myself for not being there, as I often did help him close for the night, since I would have been armed as is my custom...