WASHINGTON, D.C. (Nexstar) — Senate Republicans introduced a new bill they say will curb mass shootings. But gun control advocates say the Republican-sponsored gun legislation doesn’t go far enough.

After 2 mass shootings in his home state this summer, Texas Republican Senator John Cornyn says he returned to Washington with a heavy heart.

This week he introduced The Response Act — a bill he says will prevent other communities from going through similar heartbreak.

The bill tackles a list of factors like expanding access to mental health care, cracking down on unlicensed gun dealers, and speeding up the death penalty process for people convicted of mass terrorism crimes.

But Kris Brown with Brady United Against Gun Violence says the gun legislation isn’t enough.

“He seems to be bending over backwards to identify various solutions. None of which has anything to do with how to actually stop mass shootings. You can’t address this problem without addressing easy access to guns,” says Brown.

Brown says Congress needs to focus on taking guns away from dangerous people — not just flagging them to authorities.

But Cornyn disagrees, saying: “I don’t believe that restricting the constitutional rights of law abiding citizens is going to make our community safer.”

 Right now, Cornyn’s bill has no democratic support.