Brady United vice president for policy Christian Heyne has a message for Republican senators: Voting for gun safety legislation will help them at the polls, and they don't have to compromise on the Second Amendment to do it.

"They are in a historic moment where they can work and make the government work the way that most Americans want it to… to protect Americans from the scourge of gun violence," Heyne said in an interview with Fox News Digital, "while at the same time ensuring that law-abiding responsible, gun owners are still able to exercise their Second Amendment rights."

Heyne, whose group for decades has been on the forefront of the movement calling for gun control, is not the only person who thinks Congress may be positioned to pass something. Sen. Chris Murphy, D-Conn., said Monday that he's "more hopeful for success than ever before." 

Uvalde, Texas, school shooting memorial

Wooden crosses are placed at a memorial dedicated to the victims of the mass shooting at Robb Elementary School on June 3, 2022, in Uvalde, Texas. (Alex Wong/Getty Images)

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Murphy is leading talks in the Senate on possible gun reform, along with Sen. John Cornyn, R-Texas, who was deputized by Senate Minority Leader Mitch McConnell, R-Ky., for the job. 

The fast-moving talks come after several mass shootings in recent weeks. The one that appeared to truly kick the negotiations into high gear was a school shooting that killed 21 in Uvalde, Texas. 

Several other senators are actively involved in the negotiations, including Kyrsten Sinema, D-Ariz., Thom Tillis, R-N.C., and Susan Collins, R-Maine.

WASHINGTON, DC - AUGUST 04: Sen. John Cornyn (R-TX) speaks on a proposed Democratic tax plan, at the U.S. Capitol on August 04, 2021 in Washington, DC. The Senators spoke out tax proposal saying that it will hurt job growth and the middle class. (Photo by Kevin Dietsch/Getty Images)

Sen. John Cornyn at the U.S. Capitol on Aug. 4, 2021. (Kevin Dietsch/Getty Images)

"I think what is abundantly clear is that this is a historic moment where elected officials on both sides of the aisle are feeling the pressure to do something… on gun violence now," Heyne said. He added that the kind of "mass casualty" events like the massacre in Uvalde are "uniquely American" and said any provision that could "save a single life" would be "worthwhile."

The GOP members of the group working on a deal say they're invested in finding something at least 10 Republican senators can agree on in order to break the 60-vote filibuster threshold in the Senate. 

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"If we reach an agreement, law-abiding gun owners will not be impacted at all," Cornyn said on the Senate floor Monday. 

At least 18 students and 1 teacher were killed when a gunman opened fire at Robb Elementary School in Uvalde according to Texas Gov. Gregg Abbott. Students from the school were evacuated to the civic center.

People leave the Uvalde Civic Center Tuesday, May 24, 2022. (AP Photo/Dario Lopez-Mills)

But while legislation encouraging state red flag laws and possible background check reform appears to be in the mix, along with a combination of mental health or other measures, it's not clear the votes are there. A GOP aide told Fox News getting 10 Republicans to support a bill "will require threading the needle."

Heyne, however, says if enough Republicans do vote for legislation to help potentially curtail mass shootings, they'll be rewarded, not punished, by voters.

"If they do what is right and explain specifically why they're doing it, I firmly believe that they will be rewarded," he said. "That they will win re-election because of their position on these issues, not in spite of them."

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He added: "As far as motivating, wedge issues that will drive people to the polls, any candidate that is running on a strong gun violence prevention platform regardless of where their district is, can make a huge impact in their race."

The U.S. Capitol in Washington

The U.S. Capitol in Washington (Kelly Laco/Fox News)

Red flag legislation is something that Heyne specifically said Republicans may be able to support. He said multiple GOP governors, including now-Sen. Rick Scott, R-Fla., signed similar laws after the 2012 Sandy Hook massacre in Connecticut. He said such a proposal would likely be crafted in the image of widely accepted domestic violence statutes, creating a civil procedure that would respect due process. 

But there will be major headwinds to the effort. The majority of Senate Republicans appear to be resistant to any new laws on guns, citing concerns about violating the Second Amendment or due process rights. 

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In the immediate aftermath of the Texas shooting, Sen. Josh Hawley, R-Mo., said red flag laws, even on a state level, are "concerning." Sen. John Hoeven, R-N.D., said he would support hardening school security, as did Sen. Cynthia Lummis. R-Wyo. 

But asked if she would support any legislation that would add rules or regulations to gun ownership, Lummis said, "No."

Fox News' Kelly Phares contributed to this report.