Democrats moved quickly to clear the way for votes on legislation to strengthen background checks for gun purchasers.

Within hours of the shooting in Uvalde, Senator Chuck Schumer, Democrat of New York and the majority leader, moved to clear the way to force votes in coming days on legislation that would strengthen background checks for gun purchasers, pushing to revive measures with broad appeal that Republicans have blocked in the past.

The pair of bills would expand criminal background checks to would-be gun buyers on the internet and at gun shows and lengthen the waiting period for gun buyers flagged by the instant background check system to allow more time for the F.B.I. to investigate. The measures, passed by the House in 2019 and again last year, have languished in the Senate amid Republican opposition. Even as they publicly mourned the massacre that killed 19 children and two adults on Tuesday, Republican senators gave little indication that their positions had changed.

But some Democrats said they saw hope for bipartisan consensus on proposals that polls show have overwhelming support among Americans. And in any case, many were clamoring to force Republicans to go on the record on the measures at a time when grief and anger about gun violence in America has erupted anew following Tuesday’s massacre and a recent mass shooting that killed 10 at a Buffalo supermarket.

“What are we doing?” Senator Chris Murphy, Democrat of Connecticut, asked in an emotional speech on the Senate floor. “Why do you spend all this time running for the United States Senate? Why do you go through all the hassle of getting this job, of putting yourself in a position of authority, if your answer is that as the slaughter increases, as our kids run for their lives, we do nothing?”

Mr. Murphy, who began pushing for gun safety and background check legislation after the massacre at Sandy Hook Elementary School in Newtown, Conn., said after his speech that he believed there were 10 Republican votes to strike a deal that could move through the 50-50 Senate, where 60 votes are needed to overcome a filibuster.

But it was not clear whether that was the case, or how quickly Democrats planned to move.

“I’m outraged, I’m hurt, and I believe that this could be our undoing, if we can’t protect our children,” said Senator Cory Booker, Democrat of New Jersey.

Republicans, even as they expressed horror about the shooting, did not signal that they would drop their longstanding opposition to gun safety measures.

Senator Mike Rounds, Republican of South Dakota, said “it’s one thing to say that, regardless of the facts, you should just do something. The question is whether something you would do would actually make a difference.”

Speaking to reporters on Capitol Hill, Senator Ted Cruz, Republican of Texas, blamed Democrats “and a whole lot of folks in the media” for rushing to “try to restrict the constitutional rights of law abiding citizens.”

Senator Joe Manchin III of West Virginia, a centrist Democrat who has unsuccessfully tried to win enough support for legislation to strengthen background checks for gun purchasers, lamented the polarization in Congress that stymied his efforts and others.

“It makes no sense why we can’t do common sense things to try to prevent some of this from happening,” Mr. Manchin said. “It’s just unbelievable how we got here as a society.”

But he stopped short of supporting what could be the only path to doing so, telling reporters he maintained his opposition to doing away with the filibuster to get around Republican opposition and pass such legislation with only Democratic votes.

“You would think there’d be enough common sense,” Mr. Manchin said. “The filibuster is the only thing that prevents us from total insanity.”