Congressional Republicans are escalating their efforts to authorize the building of President Trump’s planned ballroom at the White House in the aftermath of the attack on a press gala in Washington on Saturday night that exposed security vulnerabilities.

Senator Lindsey Graham, the South Carolina Republican who chairs the Budget Committee, said on Monday that he wanted Congress to move legislation as quickly as possible to provide $400 million for construction of a secure White House ballroom that would also house national security facilities beneath it.

“We saw Saturday that America has a problem,” Mr. Graham told reporters. “That problem is, it is very difficult to have a bunch of important people in the same place unless it is really, really secure.”

Other Republicans were weighing in as well. Representative Lauren Boebert of Colorado said she planned to propose legislation this week that would give the go-ahead for the project, as did Senator Rand Paul of Kentucky, the chairman of the Homeland Security Committee.

Senator Tim Sheehy, Republican of Montana, said he would take to the Senate floor to try to win quick unanimous approval of the ballroom construction, an effort likely to run into Democratic opposition.

“It is an embarrassment to the strongest nation on earth that we cannot host gatherings in our nation’s capital, including ones attended by our president, without the threat of violence and attempted assassinations,” Mr. Sheehy said on the social media platform X.

Mr. Trump plunged ahead with his ballroom project without any congressional approval of the project or the demolition of the historic East Wing that made room for it. A federal judge halted the work, saying that the construction had not won the necessary go-ahead from Congress, which typically would provide the money and some oversight, although an appeals court allowed construction to continue while it reviews the decision.

Within hours of the attack at the annual gala at the Washington Hilton, Mr. Trump and his allies said the foiled effort nonetheless showed the need for a highly secured structure that could host such events safely.

Republican lawmakers agreed.

“By funding these necessary upgrades to the ballroom and the White House’s security infrastructure, President Trump and future presidents will be able to host large events without having to leave the White House grounds,” said an announcement by Mr. Graham, Ms. Britt and Senator Eric Schmitt, Republican of Missouri.

The episode at the hotel on Saturday also spurred more calls to end a shutdown at the Department of Homeland Security that has lasted for more than 70 days. House Republicans have so far refused to take up a bipartisan Senate bill that would fund much of the agency outside immigration enforcement, despite earlier agreement by Speaker Mike Johnson to do so.

Mr. Johnson said on Monday that he was not ready to bring the bill to the House floor and wanted to make some “modifications.” If such a measure could make it through the House, the Senate would then have to pass it for the third time.

Senator Chuck Schumer of New York, the Democratic minority leader, said Republicans should focus on passing that legislation, which includes money for the Secret Service, instead of a new White House party space.

“If Republicans truly want to improve security, they should join Democrats in funding the Secret Service, not Donald Trump’s luxury ballroom,” Mr. Schumer said Monday.

Mr. Trump never sought congressional authorization for the ballroom project and said he would spare taxpayers the expense by relying on private donations. That raised questions about donors trying to curry favor with the administration through the project. Mr. Graham said he wanted the ballroom and adjacent facilities to be paid for with public dollars that would be offset by other federal fees, adding that private funding should be used for extras such as china.

Should Congress ultimately provide money and the authority for the job, it could also give lawmakers more say-so in the work — oversight that could meet White House resistance.

Representative Hakeem Jeffries, Democrat of New York and the minority leader, criticized the ballroom as “a vanity project” and argued that Republicans were improperly focused on an issue that would not address more pressing concerns of the American people.

“I have not seen a specific request with respect to the ballroom, but needless to say, we have to drive down the high cost of living,” he said at a news conference. “Life has become more expensive as a result of Donald Trump and Republican policies over the last 15 months.”

But Mr. Graham and other Senate Republicans sought to dispel the notion that the ballroom was a presidential vanity project, saying the real beneficiaries would be future presidents given the time line for construction.

“This is not about Trump. It’s about the presidency of the United States,” Mr. Graham said. “It is about the person who occupies that office not being put at risk if they choose to go off campus.”

The dinner that for decades has taken place at the Washington Hilton is sponsored by the White House Correspondents’ Association, a group of journalists who cover the White House, not by the administration. It is unclear whether the association would agree to hold such an event on the White House grounds.