President Biden’s demand for new gun control measures on Tuesday was the latest in what has become a doleful ritual in Washington: making a renewed call for legislation after a deadly mass shooting, the latest one at a Colorado grocery store where 10 people, including a police officer, were killed on Monday.
But while polling regularly shows broad support for tighter gun laws and specific policies like a ban on assault weapons, Republicans in Congress remained all but immovable on the issue, repeating longstanding arguments on Tuesday that gun violence should be addressed through steps like more policing rather than limiting gun rights.
“There’s not a big appetite among our members to do things that would appear to be addressing it, but actually don’t do anything to fix the problem,” said Senator John Thune of South Dakota, the No. 2 Senate Republican.
Even before the recent shootings, which also included a deadly rampage at massage parlors in Atlanta, Democrats had begun advancing stricter gun control measures. But those proposals face long odds in the 50-to-50 Senate, where it takes 60 votes to overcome a filibuster.
House Democrats passed two bills this month aimed at expanding and strengthening background checks for gun buyers by applying them to all gun buyers and extending the time the F.B.I. has to vet those flagged by the national instant check system.
The twin pieces of legislation passed in the House have been deemed ineffective and too expansive by most Republicans; only eight House Republicans voted to advance the universal background check legislation. The bills would almost certainly not muster 60 votes in the Senate.
Nevertheless, Senator Chuck Schumer, Democrat of New York and the majority leader, vowed on Tuesday to put the bills to a vote on the Senate floor, and Mr. Biden urged their passage while also calling for an assault weapons ban. The gunman in the Colorado shooting was armed with both a military-style semiautomatic rifle and a pistol.
Senator Mitch McConnell of Kentucky, the Republican leader, said that he was “open to the discussion” around gun control measures, but that he was opposed to the two House-passed bills.
“What I’m not attracted to is something that doesn’t work, and there have been deep-seated philosophical differences between Republicans and Democrats about how to deal with gun violence,” Mr. McConnell said.
Mr. Biden, for his part, expressed uncertainty when asked by a reporter whether he had the political capital to move forward with gun safety measures.
“I hope so,” he said, crossing his fingers. “I don’t know. I haven’t done any counting yet.”