The 2nd Amendment's not going away, but neither are these mass murders. For me finding a middle ground absolutely needs to start with lifting the absurd, pathetic federal ban on the CDC collecting any data or conducting any studies about the effects of gun violence. Can't fix the problem if we can't study it. There also needs to be a dialogue between lawmakers, responsible gun owner groups (aka not the NRA), and researchers about the solutions best able to reduce not just the big public attacks but everyday killings as well.
To me that includes a focus on eliminating background check and transfer loopholes (not many left though), registering guns, closing bizarre discrepancies like the one that let a Florida 19-year-old buy an AR-15 but not a handgun. Then reducing the number of rounds one person can fire over a given amount of time. Smaller clips/magazines, banning accessories designed to increase firing rate, etc.
I'm not keen on the mental health angle - the vast majority of mentally ill people are not a threat, and they're statistically more often the victims of gun crime than the perpetrators. It'd also add a legal stigma to being diagnosed that could discourage people from seeking treatment. I might be ok with the extreme cases Obama's regulation targeted, but I'd really need a hard look at it and it's unlikely to make too much of a dent. I'd like to see more resources devoted to law enforcement identifying people like this shooter in advance, but there's only so much they can do before there's evidence of a serious crime.
However it ends it all starts with driving out the craven, absurd line of rhetoric that argues these killings are completely inevitable and America simply has to lay down and take it, and starting to center our political debates around how to minimize these horrors rather than whether we can do anything about it at all.