WASHINGTON (AP) — Less than 48 hours after a gunman stormed an elementary school and killed 19 children and two teachers in his home state of Texas, Sen. John Cornyn walked straight from the floor of the U.S. Senate into Republican leader Mitch McConnell's office.

The Texas Republican had just returned to Washington from the scene of the horrific school shooting in Uvalde when he was summoned by McConnell to lead the GOP in fraught negotiations over a potential legislative response to the tragedy. Eager, if wary, he took the job.

"I'm not interested in making a political statement," Cornyn said at the time. "I'm actually interested in what we can do to make the terrible events that occurred in Uvalde less likely in the future."

Cornyn is at the center of a bipartisan group of senators working furiously to try to strike a compromise over gun safety legislation, a political longshot despite the heartbreaking pleas from the Uvalde community to "do something" after the massacre.

A four-term senator, Cornyn has been here plenty of times before, a central figure at the forefront of on again, off again talks with Democrats over gun policy changes that almost never make it into law. As gun owners and the powerful gun lobby wield influence, Congress has proven unable to substantively respond even as more gruesome mass shootings rip through communities all across America.

With his previous negotiating partner, Sen. Chris Murphy-D-Conn., Cornyn convened a small group of four senators to meet privately this week, some who are part of a broader Murphy-led group in a desperate search for possible compromise gun safety measures.

President Joe Biden implored Congress — and particularly the Republican senators, who have spent years blocking almost every gun control measure — to act.

"This time, it's time for the Senate to do something," Biden said in remarks from the White House.

Biden, too, is looking at Cornyn to lead.

"I think there's a realization on the part of rational Republicans — and I think Senator McConnell is a rational Republican; I think Cornyn is as well — I think there's a recognition in their party that they — we can't continue like this," Biden said earlier in the week after visiting Texas.

Expectations are low that even the most modest gun control measures could find support among Republicans in Congress, particularly in the evenly-split 50-50 Senate where at least 60 votes are needed to advance legislation past a filibuster.

Senators aren't expected to even broach ideas for an assault weapon ban or other restrictions that are popular with the public as potential ways to curb the most lethal mass shootings.

Instead, the bipartisan group is intensifying talks to reach a deal on incremental changes to the nation's gun laws, after a decade of mostly failed efforts ever since a gunman killed 20 children at Sandy Hook Elementary School in Connecticut.

At most, the senators may be able reach consensus in a few distinct areas — bolstering school security measures; adding more mental health resources in communities; and possibly sending money to the states to encourage red flag laws to keep firearms out of the hands of those who would do harm.

"That may be all they can do," said Matthew Bennett, a longtime gun policy advocate at the centrist Third Way think tank.

It's been nearly 30 years since Congress approved sweeping gun safety legislation with the passage of the 1994 assault weapons ban, which has since expired. In 2013, Congress rejected proposals to expand background checks and ban some assault-style rifles and high-capacity ammunition magazines.

One of the only gun-related bills that has become law in the decade since the 2012 Sandy Hook massacre was Cornyn's fix-NICS bill — a modest effort he and Murphy developed to encourage states to comply with the recordkeeping of the National Instant Criminal Background Check System.

Cornyn first pushed the bill forward after another tragedy in his state, the 2017 church shooting in Sutherland Springs, Texas, when the gunman's Air Force record of court-martial for domestic violence had not been sent for inclusion in the federal database used for gun purchases.

The Fix-NICS bill stalled in the Senate, until months later when another gunman opened fire at a Parkland, Florida, high school killing 17 in a massacre on Valentine's Day in 2018.

"Let's do what we can and build from there," Cornyn said at the time.

But by then, Democrats and some Republicans were circulating broader proposals and Donald Trump, who was president, suggested raising the legal age for purchasing firearms to 21. But efforts fizzled after Trump had an Oval Office meeting with the National Rifle Association.

The Fix-NICS bill ultimately won approval in Congress not on its own, but after being included in a government funding measure later that spring. It had the NRA's backing.

Cornyn, who has an A+ rating from the NRA's Political Victory Fund for his support of Second Amendment issues, said last week the Uvalde killings may be an impetus for new reforms.

A former judge and member of the Texas Supreme Court, Cornyn, 70, is a member of McConnell's leadership team and widely believed to be a contender to become Republican Senate leader whenever McConnell retires. McConnell tasked him to work with Murphy and also Democratic Sen. Kyrsten Sinema of Arizona, a deal-maker close to Republicans.

An owner of multiple firearms who frequently hunts in Texas, Cornyn did not attend the NRA's convention in Houston alongside Trump and fellow GOP Texas Sen. Ted Cruz in the days after the Uvalde shooting, even as he dismissed some of the red-flag laws or broader changes in federal gun policy being proposed.

"He is the central figure — or at least one of them — because he has respect among Republicans but is also a critical thinker," said Sen. Richard Blumenthal, D-Conn., about Cornyn.

"If he really wants to get it done, he will potentially make a critical difference."

Many Democrats are skeptical that Republicans in the Senate will come to the table. Already the Senate has hopelessly blocked two House-passed measures to bolster background checks for firearm purchases online or at gun shows.

Instead, House Democrats are pushing ahead with their own package of gun safety measures, the "Protecting Our Kids Act," that includes raising the age limits on semi-automatic rifle purchases from 18 to 21 years old. It has almost no hope of passing the Senate.