Lawmakers note 'profile' of mass shooters -- mostly young men -- as they weigh gun compromise

Bipartisan talks about passing a new federal gun law continued through Memorial Day weekend despite members of Congress being out of session in a weeklong recess that also set a deadline for a possible breakthrough, Connecticut Sen. Chris Murphy said on Monday.

In a tweet, the lead Democrat on the negotiations wrote that he and others in his party have discussed with some Republican Senate colleagues throughout the holiday weekend details of possible bill intended to address gun violence.

The Senate left Washington on Thursday, with Majority Leader Chuck Schumer, D-N.Y., indicating a short turnaround for the compromise legislation -- members would vote upon a June 6 return to the chamber.

"In between parades, I've been on the phone today w Republican and Democratic Senators trying to find the common denominator on a gun violence bill," Murphy wrote on Twitter on Monday. "Senator Schumer has given us just over a week to find a compromise. This time, failure cannot be an option."

Senate Minority Leader Mitch McConnell has blessed the negotiations, tasking Republican Texas Sen. John Cornyn to take the lead for the GOP in the talks. Murphy has said that in the wake of two high-profile mass shootings over the past few weeks, "many more" Republicans appear willing to discuss gun reform than in the past.

While the issue remains intensely divisive in Congress -- where conservatives have opposed major legislative efforts regarding guns -- Cornyn echoed Murphy on Monday in saying that, at the least, the talks were ongoing. "We're already having those discussions in person and on the phone. Look forward to meeting on Tuesday through a Zoom call to try to see if we can agree on a basic framework about how we go forward," he said.

Murphy told ABC "This Week" co-anchor Jonathan Karl on Sunday that the negotiations were "serious" and already circling some specifics, including so-called "red flag" laws that would allow the removal of firearms from people with a history of threatening or dangerous behavior.

"We have continued to work throughout the weekend. I was in touch with Sen. Cornyn and Sen. [Pat] Toomey, other Republicans and Democrats yesterday," said Murphy, who represents the community that includes Sandy Hook Elementary School, site of a 2012 mass shooting.

"Inside this room we're talking about 'red flag' laws, we're talking about strengthening, expanding the background check system, if not universal background checks. We're talking about safe storage," Murphy said, noting that school safety measures and mental health resources were also discussed.

There has been talk about the "profile" of mass shooters, Murphy said -- in particular the pattern of many of the perpetrators to be young men between 18 and 21 years old.

"Right now we're having a discussion inside this room about the profile of the current mass shooter ... That is a profile that does not allow you to buy a handgun but does allow you to buy an assault rifle. And so there are discussions happening in these rooms about how they recognize this profile and maybe make it a little bit harder for those individuals to quickly get their hands on weapons," Murphy said.

"I don't yet know exactly what's possible, whether the votes are there to raise the age, but we're having a discussion about what we do about that specific profile," he said. "And it's an encouraging conversation."

Murphy, elected to the Senate in 2012, drew new attention in the wake of the Uvalde, Texas, elementary school shooting last week that left 19 students and two teachers dead. One of Congress' most outspoken voices for gun control, Murphy again urged action including from Republicans, many of whom contend the laws are misplaced or violate the Second Amendment.

On "This Week," Murphy reiterated his concern with the lack of federal legislation on the issue in the near-decade since Sandy Hook -- a period that has also been stained by a slew of other high-profile mass shootings.

"And while, in the end, I may end up being heartbroken, I am at the table in a more significant way right now with Republicans and Democrats than ever before," Murphy said. "Certainly, many more Republicans willing to talk right now than were willing to talk after Sandy Hook."

Murphy pointed to his recent discussions with Republican Sen. Rick Scott of Florida, who now represents in Congress the site of another school shooting, in Parkland, where a gunman shot and killed 17 students and staff members at Marjory Stoneman Douglas High School in 2018.

Following that massacre, then-Gov. Scott signed into law a bill that tightened gun control measures, including raising the minimum age for owning guns from 18 to 21.

"I had a long conversation with Sen. Scott last week," Murphy said, "and had him tell me the story of how they were able to pass that legislation and get Republicans to support it."

ABC News' Trish Turner contributed to this report.