"Core four" emerges on bipartisan gun talks

Sens. Chris Murphy (D-Conn.), John Cornyn (R-Texas), Kyrsten Sinema (D-Ariz.) and Thom Tillis (R-N.C.) met virtually via Zoom on Tuesday to discuss a legislative response to the school shooting in Uvalde, Texas.

State of play: The talks have so far centered largely on mental health, with gun reform and school safety likely to be smaller components of any bill, two sources familiar with the meeting tell Axios.

• Senate Minority Leader Mitch McConnell told reporters in Kentucky on Tuesday that he hopes senators can come together to "target the problem, which is mental illness and school safety."
• McConnell, who has directed Cornyn to work with Democratic lawmakers on a "bipartisan solution," did not mention guns.

Why it matters: The potential legislation would be hyper-focused and targeted to something that can realistically pass, meaning it would fall short of a package that most Democrats want.

What we're hearing: Murphy, Cornyn, Sinema and Tillis are now being seen as the "core four" in the negotiating process. Members of the larger bipartisan group that met in the Capitol last week, which includes an additional three Democratic and four Republican senators, are expected to meet virtually later this week.

• Those members include Sens. Joe Manchin (D-W.Va.), Richard Blumenthal (D-Conn.), Martin Heinrich (D-N.M.), Lindsey Graham (R-S.C.), Susan Collins (R-Maine) and retiring Sen. Pat Toomey (R-Pa.).

Details: The talks are still in the early stages, with the substance of any potential deal still very much in flux. But the senators who met Tuesday are still encouraged they will be able to reach a compromise that can get at least 60 votes, if not more — especially if Cornyn signs on, the sources said.

• Murphy is being very realistic as to what can actually pass, a position that has encouraged the more moderate and conservative members of the group.

What they're saying: "I’m sober-minded about our chances. ... My hope is that the increased number of people willing to talk matters," Murphy said in Connecticut on Tuesday.

• "Senators Murphy, Sinema, Tillis and I had a very constructive conversation about the best response to the horrific events in Uvalde last week," Cornyn said in a statement.
• "We’ve asked our staff to continue to work together to address some of the details that we hope to be able to discuss at some point soon."

Timing: The group's goal is to reach a compromise before the Senate returns from its Memorial Day recess on June 6.

• Senate Majority Leader Chuck Schumer has given Murphy the space he needs to make a deal but has also made clear he will not let these talks drag on.