It's funny because arguably, the NRA has been fighting measures to better the background check system.
I keep bringing up the fact that after the Assassination attempt on Regan, the Brady Hand Gun Bill was introduced and largely passed into law. The problem is that there was a specific part of it that required states to submit felony and mental health records to the background check system. The NRA lobbied against that and it was subsequently thrown out by the Supreme Court.
The ATF hasn't had a permanent department head since 2006 thanks to the NRA and allies.
The Tiahart Ammendment does not let the ATF require inventory checks to detect lost or stolen guns, they can't use the trace data to find and shut down shady gun dealers.
The Senate confirmed an ATF chief 3 days before the Navy Yard shooting, actually.
And it terms of the mental health records, it's not as simple as you think because of doctor patient confidentiality laws.