Sen. Chris Murphy, D-Conn., addresses a rally with fellow Senate Democrats and gun control advocacy groups outside the U.S. Capitol on Thursday. Organized by Moms Demand Action, Everytown for Gun Safety and Students Demand Action, the rally brought together members of Congress and gun violence survivors to demand gun safety legislation following mass shootings in Buffalo, N.Y., and Uvalde, Texas.

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Sen. Chris Murphy, D-Conn., addresses a rally with fellow Senate Democrats and gun control advocacy groups outside the U.S. Capitol on Thursday. Organized by Moms Demand Action, Everytown for Gun Safety and Students Demand Action, the rally brought together members of Congress and gun violence survivors to demand gun safety legislation following mass shootings in Buffalo, N.Y., and Uvalde, Texas. / Getty Images

Senators are expected to continue talks next week to try to develop new gun legislation in response to the Robb Elementary School shooting in Uvalde, Texas, that killed 21 people, 19 of them children.

They're racing against a self-imposed deadline set by Democrats to reach a deal by the time the Senate returns from its Memorial Day recess on June 6.

It's not clear a deal can be reached soon. The Senate will be in recess next week and the momentum could wane, but lawmakers, led by Democratic Sen. Chris Murphy, are still pushing ahead on talks in the hope of being able to take some action.

"I know this is a moment where a lot of people feel a sense of hopelessness, I know folks feel this moment of deja vu," Murphy told a crowd of gun violence survivors and advocates for reform legislation outside the Capitol. "But what I also know is that the great social change movements in this country, the ones you read about the history books, they don't succeed in a year or two years. They often take time."

For those gun control advocates, a bipartisan effort to find common ground has been a long time coming. In the days after the shooting in Uvalde, demonstrators — who included gun violence survivors — at the Capitol sought to put pressure on lawmakers. As is often routine, only Democratic lawmakers were there to greet them.

"It is crippling to be this angry and this infuriated by the lack of action by the people who hold all the power," said New York Democratic Sen. Kirsten Gillibrand.

While her party holds control of the White House and Congress, they fall 10 votes short in the Senate to approve bills to address the country's mass shootings. And skepticism to overcome that gap runs deep in Congress and beyond.

On the Senate floor, Senate Majority Leader Chuck Schumer says while Democrats have been burned before, they're going to try for a deal with the GOP again.

"Not trying everything is not acceptable to the families who have lost their loved ones," he said.

Schumer now says if these new talks fail, a vote will be on tap regardless to show where every senator stands.

"I want to be clear this is not an invite to negotiate indefinitely," he said.

One of those key negotiators is Texas Republican Sen. John Cornyn, who visited the scene of the shooting in Uvalde. Cornyn has led past negotiations for Republicans on narrow limits to gun access.

Senate GOP leader Mitch McConnell said he encouraged Cornyn after his Texas trip to negotiate with Democrats.

Cornyn and other Senate Republicans, such as Maine's Susan Collins and North Carolina's Thom Tillis, have been in discussions with Murphy.

Murphy, like those Republicans and more, says there could be a shot at a limited deal.

"We will be engaged in bipartisan conversations to try to find a path forward," Murphy said.

Murphy was elected to Congress just before the deadly shooting at Sandy Hook Elementary in his home state 10 years ago and has worked since on gun control measures.

He admits it can be a long and arduous journey, but says that relentless commitment is what leads to major social change.

"Sometimes they take a decade or more. Sometimes they get met with these huge obstacles, these setbacks," Murphy told the crowd of survivors outside the Capitol, referring to those behind great social change movements. "But they are so confident that the status quo will finally break that they never ever give up and we are never ever giving up."

The coming days will dictate if both parties can reach a bipartisan deal, or once again, serve as a reminder that Congress is too divided to stop future attacks.

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