I don't doubt this to be true, but I have to admit I'd be pissed if I was a "responsible, law-abiding" gun enthusiast and the government outlawed guns I owned. It would be like the government taking my skis or telling me I couldn't ski in a certain area because of all of the recent avalanche deaths.
That said, I see no downside to a policy, similar to the one Tvash outlined, that makes guns harder to get and easier to track and regulate.