Two of the top Senate Democrats leading the charge for gun control legislation in the wake of the Uvalde, Texas, school shooting said Thursday that there may be enough Republican support for some kind of measure to pass. 

Sens. Chris Murphy, D-Conn., and Richard Blumenthal, D-Conn., made the comments after a rally with gun control supporters outside the U.S. Capitol Thursday. This comes as multiple top Senate Republicans are indicating they may support some kind of legislation after 21 people died in the attack on Robb Elementary School this week. 

"There are at least six to 12 who have gone beyond general expressions of interest to looking at drafts and language in statute that could pass," Blumenthal said. "I'll let them announce when they're ready who they are. But this next week will be a testing time because we'll see who exactly is willing to put signatures on paper."

Texas school shooting police officer lights candle

A man lights a candle outside Robb Elementary School in Uvalde, Texas, Wednesday, May 25, 2022. (AP Photo/Jae C. Hong)

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Murphy, who is considered the leader of the negotiations on the Democrat side, said there will be bipartisan meetings on the matter Thursday, and that talks will continue over the Senate's Memorial Day recess. 

But, he said, Republicans will have a limited time to agree to something, or else Democrats will start forcing tough votes on the Senate floor. 

"We need at least a week to work through these tough issues. Frankly, sometimes, it's easier to work those issues outside of Washington rather than when we're here," Murphy told reporters. "We love you guys, but sometimes it's a little bit easier to negotiate with each other rather than negotiate through the Washington, D.C., press."

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)

"We'll have a series of meetings today to set the table for next week, and then we'll work really hard to try to find a bipartisan product," Murphy added. "But listen, I'm not gonna negotiate forever… So if we can't get some progress by the end of next week, then I'll say to Sen. Schumer, it's time to take votes."

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In remarks to supporters from Moms Demand Action and Everytown during the rally outside the Senate, Murphy also emphasized that Democrats will make Republicans take difficult votes if they don't play ball on gun reform. 

"We are going to force people to tell America which side they are on," Murphy said. 

Blumenthal and Murphy were joined Thursday by other lawmakers, including Sens. Amy Klobuchar, D-Minn., Ed Markey, D-Mass., and Alex Padilla, D-Calif. 

Sen. Ed Markey guns

Sen. Ed Markey speaks at a gun control rally outside the Captiol on May 26, 2022. (Tyler Olson/Fox News)

A rowdy crowd a few hundred feet from the senators chanted "now" and "action," demading that the Senate – and Republicans in particular – pass some form of gun legislation. 

"How is this acceptable?" Padilla said of school shootings like the one in Uvalde, Texas, in a comment directed at Republicans. "How are you not outraged?"

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Markey, meanwhile, called for the packing of the Supreme Court so that the justices would not be able to overturn any Democrat-passed gun laws, and he told activists not to let the momentum on the gun issue die down. 

"This time is different," he said. "If you do not change your mind, the American people are gonna change you are their representative."

But the task of passing anything in the Senate – during an election year, as politics is as polarized as ever – particularly on guns, is extremely tall. 

Senate Majority Leader Chuck Schumer, D-N.Y., forced a procedural vote Thursday on a bill directed at White supremacist terrorism. The legislation was initially meant to address the mass shooting at a Buffalo, New York, supermarket earlier this month. But Schumer said he would use that bill, if it cleared a 60-vote procedural hurdle to start debate, as a vehicle for gun-related amendments too. 

But the vote failed 47-47 Thursday, with all Republicans opposing it. Schumer switched his vote to be against the bill to potentially bring it back to the floor at a later time. 

There is some optimism from a few top Republicans that something could get done on gun control this year. 

"This a new development. Buffalo's a new development," Sen. John Cornyn, R-Texas, said Thursday. "I think there's a sense of urgency that maybe we didn't feel before but so, we're gonna try. I mean, that's all we can do is try and that's what we're, what I'm gonna do."

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Senate Republican Policy Chair Roy Blunt, R-Mo., also said Wednesday that he could be supportive of a red flag law. 

But many other Republicans appear resistant to any gun legislation. Asked Wednesday whether there is any new regulation on guns or gun ownership that she could support, Sen. Cynthia Lummis, R-Wyo., responded, "No."

Fox News' Thomas Phippen and Jason Donner contributed to this report.