The "increase access to mental health care" strikes me as a somewhat more palatable version of the same process that gives us the "arm teachers" response. People have been forced to acknowledge that SOMETHING needs to be done, but they don't want that something to be "restrict access to guns", so they're trying to come up with alternatives.

(Don't get me wrong, I'm all in favour of improved mental health care, but doing it as a response to Newtown is more likely to stigmatise mentally-ill people than benefit them, and it's not guaranteed to fix the problem. AFAICT we still don't have any confirmation that the shooter was diagnosably mentally ill.)