A bipartisan group of senators is hoping to nail down a framework for new gun safety legislation this week, some key negotiators said Sunday, and they are cautiously optimistic that after a recent spate of mass shootings, Congress might actually take action this time. The changes wouldn’t be as far-reaching as those called for by President Biden in a national address last Thursday. Instead, the goal is to find legislation that 10 to 20 Senate Republicans will support.

The “intensive” bipartisan negotiations don’t “guarantee any outcome,” Sen. Pat Toomey (R-Pa.) told CBS’s Face the Nation. “But it feels to me like we are closer than we’ve been since I’ve been in the Senate.” Toomey co-led an unsuccessful effort to expand background checks in 2013, after the Sandy Hook school shooting in Connecticut. These talks are being led by Sen. John Cornyn (R-Texas) and Sen. Chris Murphy (D-Conn.). 

“It’s really tough sledding,” Murphy told The Washington Post on Sunday. “But I’ve never been part of conversations that are this serious and this thoughtful before, and I know all the Republicans and Democrats who are at the table are there with total sincerity to get an agreement.”

A group of more than 250 conservative gun enthusiasts in Texas, including prominent GOP donors, signed a full-page ad in Sunday’s Dallas Morning News backing Cornyn’s negotiations and an expansion of background checks and “red flag” laws after the mass murder of 19 children two teachers in Uvalde, Texas. Polls consistently show strong public support for new gun safety laws, especially expanding background checks.

Murphy said Senate negotiators are looking at the package of measures Florida’s Republican legislature passed in 2018 after the Parkland school shooting, signed into law by then-Gov. Rick Scott (R), now a senator. That package provided funds mental health and security at schools, created a red flag law and a three-day waiting period, and raised the minimum age to purchase AR-15 rifles and other long guns to 21 from 18. 

“The template for Florida is the right one, which is do some significant mental health investment, some school safety money and some modest, but impactful, changes in gun laws,” Murphy said. “Scott passed that law in Florida because it was the right thing to do, but also because Republicans saw it as good politics. We have to make the case for Republicans that right now this is good politics.”