After Aurora, after Tucson, after Sandy Hook, after Charleston, and most recently, after Lafayette, conservative lawmakers have tended to meet outraged cries for more gun control with a counterproposal: enforce the gun laws already on the books and improve mental health care to identify and treat the next potential madman.

In Congress, however, those proposals have never quite made it into serious legislation that has earning garnered the backing of Republican leadership and key interest groups. But one prominent GOP senator is now taking a stab at reforms that, he says, have the backing of mental health and law enforcement groups and, crucially, the National Rifle Association.

The Mental Health and Safe Communities Act introduced Wednesday by Sen. John Cornyn (R-Tex.) does not include even the modest expansion to the national background check system that was at the center of the last major gun control push, which was rejected by the Senate in 2013 amid NRA opposition.

[The latest Gabby Giffords push for modest gun controls is new. The outlook isn’t.]

But the bill would clarify the types of mental health records required to be forwarded to the National Instant Criminal Background Check System -- an issue raised in the recent shooting in Lafayette, La. -- and encourage states to send more information to the database by creating a stick-and-carrot compliance system. It would also encourage "best practices" for responding to mental health crises, including the use of specially trained response teams by federal and local law enforcement agencies.

“This legislation will strengthen programs that promote preventative screening and crisis response training so that we can better understand and treat the factors which may endanger public safety,” Cornyn said in a statement. “By giving our communities the resources necessary to recognize and prevent acts of violence, we not only protect American families, but help those affected by mental illness.”

[Lafayette shooter able to buy gun because he was never involuntarily committed]

Although Cornyn's bill might address the circumstances seen in the Lafayette case, where shooter John Russell Houser had previously had encounters with the mental health system, it would not address the background-check shortcomings exposed int he Charleston, S.C., shootings. There, the accused gunman, Dylann Roof, was allowed to buy a gun, even though pending drug charges should have barred him.

The bill is unlikely to earn many plaudits from Democrats, who generally support more robust measures to expand background checks and otherwise cut down on the availability of firearms to potential mass killers, but the NRA's backing of Cornyn's bill gives it a chance to emerge from a Republican Congress. And the fact that Cornyn is the Senate Majority Whip, is a senior member of the Judiciary Committee, and holds an A-plus NRA rating means that the bill could quickly find its way to the center of the congressional agenda -- especially if another tragedy forces it there.