Several senators are meeting to discuss potential gun control legislation Wednesday, after a separate meeting on the topic Tuesday, as lawmakers try to find common ground after last week's school shooting in Uvalde, Texas.

Punchbowl News first reported the meeting scheduled for Wednesday afternoon. Fox News confirmed the existence of the meeting, including that Senate dealmaking regulars Joe Manchin, D-W.Va., and Susan Collins, R-Maine, will be in attendance. 

Sen. Chris Murphy reacts to the Texas school shooting

Sen. Chris Murphy spoke from the Senate floor after the school shooting in Uvalde, Texas. (Senate Pool Video)

Also there leading the discussion is Sen. Chris Murphy, D-Conn., who attended the meeting Tuesday. Sens. Richard Blumenthal, D-Conn., Kyrsten Sinema, D-Ariz., Martin Heinrich, D-N.M., Pat Toomey, R-Pa., Bill Cassidy, R-La., and Lindsey Graham, R-S.C., are also attending, Fox News confirmed. 

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The Wednesday meeting will not include Sen. John Cornyn, R-Texas, who was in the smaller Tuesday meeting that included Murphy, Sinema and Sen. Thom Tillis, R-N.C. 

"Sens. Murphy, Sinema, Tillis and I had a very constructive conversation about the best response to the horrific events in Uvalde last week," Cornyn said Tuesday night. "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."

Joe Manchin speaks

Sen. Joe Manchin speaks during a Senate Appropriations Subcommittee hearing in Washington, April 26, 2022. (Jim Lo Scalzo/EPA/Bloomberg via Getty Images)

House Democrats Tuesday announced that they plan to advance a package of gun control measures this week, and set it up for a vote next week. Among the measures they plan to include are an increase in the minimum age for purchasing semiautomatic rifles, banning new high capacity magazines and tightening rules on ghost guns. 

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But the Senate talks are more limited, focusing mostly on incentivizing state red flag laws and potentially expanding background checks. Graham over the weekend expressed support for red flag legislation. 

"There are a lot of states that have red flag laws. I would support a grant program to help states that choose to go down that road," Graham said. 

Susan collins reporters

Sen. Susan Collins is surrounded by reporters as she heads to vote at the Capitol on Nov. 6, 2019. (AP Photo/J. Scott Applewhite, File)

Blumenthal, a member of the Senate Judiciary Committee, also said last week he believes there's potential for action on red flag laws. 

Despite the sense of urgency around gun reform many are feeling in the wake of the Uvalde school shooting, which killed 19 children and two adults, passing any gun bill will be a tall task with the 60-vote filibuster in the Senate. That means at least 10 Republicans will need to vote for any final bill.

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"Ten votes on the Republican side will be hard," a Senate GOP aide told Fox News about the gun talks. 

Children run to safety during a mass shooting

Children run to safety after escaping through a window during a mass shooting at Robb Elementary School in Uvalde, Texas, May 24, 2022. (Pete Luna/Uvalde Leader-News/Handout via Reuters)

"Any deal that gets 10 Rs will require threading the needle,' another Senate GOP aide said. 

But, a third Republican aide told Fox News, senators are trying to reach agreement on "a few discreet areas where improvements can be made – not some comprehensive bill that will and up in a legislative trash heap."

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Senators will likely be under a lot of pressure to come to a deal quickly, before the Uvalde shooting fades from the news cycle. Murphy said last week he expects tangible progress by the end of this week. Or else, he said, "I'll say to Sen. Schumer, it's time to take votes" on gun bills that Democrats say will put Republicans in a tough political position.