I'm not saying they would or wouldn't.
But if we agree this issue can be solved, then it will probably take compromise on both sides, and sacrifices.
It seems impossible to compromise when you start by offering a list of things you will never, ever compromise on.
I'm pro gun too, and if I heard of a decent way, I could get on board. I don't object to background checks as it is, that's not a high hurdle. Shit I don't rent apartments to people without getting a full criminal/credit/eviction background check.
I'm not real sure that would even matter. Couple that with the millions of available guns already in the American public, and I see no real solution. What's going on inside of a person's head is largely easy to hide (unless full on legit schizophrenia or whatever) and guns are too easily attainable.
Making guns illegal to own would also be fruitless. I see the hard road as the only road. I hope I'm wrong. But a real cultural change is needed. Not to get to "hippie" here, but maybe we freakin' need classes on compassion/understanding from K-12. It's a longer, harder road that way, but I don't see another way out of it all.