But since Mr. Trump named Mr. Gaetz last week as his choice to head the Justice Department, House Republicans have been reluctant to make the report public. And following an hourslong meeting on Capitol Hill of the secretive ethics panel on Wednesday, Representative Susan Wild of Pennsylvania, the ranking Democrat, said the panel had voted along party lines to not make its findings public.

In a statement on behalf of the five Democrats on the evenly divided panel, Ms. Wild said that “in order to affirmatively move something forward, somebody has to cross party lines and vote with the other side.” She noted that the panel often takes bipartisan votes. But, she said, “that did not happen in today’s vote.”

In fact, the five Republicans on the committee all voted together against releasing the report, and all Democrats voted to release it, according to a person familiar with the meeting who insisted on anonymity to discuss the confidential session.

Representative Michael Guest, the Mississippi Republican who chairs the committee, declined to comment on the session, saying only: “There was no agreement by the committee to release the report.”

Ms. Wild then made her separate statement, apparently in an attempt to make it clear that Democrats had not gone along with the decision to bury the report.

Speaker Mike Johnson pressured the committee last week not to release its findings on Mr. Gaetz, arguing that it would constitute a “terrible breach of protocol” to do so after a member had resigned, putting him beyond the panel’s jurisdiction. He also privately urged Mr. Guest not to make the findings public.

Mr. Guest told reporters earlier on Wednesday that the report was not yet finished, the main argument that Republicans had made during the closed-door session for why it should not be released, according to the person familiar with the meeting. But the panel had been set to vote last Friday on whether to release it.

That meeting was scrapped after Mr. Gaetz abruptly resigned from Congress following Mr. Trump’s announcement naming him as the pick for attorney general.

Ms. Wild said the panel would meet again on Dec. 5 to discuss the matter further.

In the Senate, Republicans and Democrats alike have demanded to see the report as part of the confirmation process. Some Republican lawmakers, like Senator John Cornyn of Texas, have suggested that the Judiciary Committee, which has jurisdiction over Justice Department nominees, could subpoena the House committee if it did not willingly hand over the file.

On Wednesday evening, Representatives Sean Casten, Democrat of Illinois, and Steve Cohen, Democrat of Tennessee, each moved to compel a vote of the full House on the matter. House G.O.P. leadership will have two legislative days to conduct the vote — either on Thursday, before the Thanksgiving recess begins, or on Dec. 3, when lawmakers return.

The drama unfolded as Mr. Gaetz accompanied Vice President-elect JD Vance across the Capitol meeting with Republican senators to win their support for his confirmation. Many senators in both parties have expressed concern over the choice of Mr. Gaetz to lead the Justice Department.

In addition to his ethical and legal challenges, Mr. Gaetz has a long record of gleefully disparaging some Republican senators whose votes he now needs to be confirmed. For instance, he has referred to Senator Mitch McConnell, Republican of Kentucky and the minority leader, as “dangerous” and coined the nickname “McFailure” for him. But on Wednesday, he was working to shore up support with Republican skeptics, including Mr. Cornyn and Senator Susan Collins of Maine.

Since the spring of 2021, the ethics panel had been investigating Mr. Gaetz over an array of allegations, including that he had engaged in sexual misconduct and illicit drug use, shared inappropriate images or videos on the House floor, misused state identification records, converted campaign funds to personal use and accepted gifts that violated House rules.

The congressional panel’s investigation paused while the Justice Department carried out a related investigation of Mr. Gaetz’s conduct, including allegations involving sex trafficking and sex with a minor. In February, the Justice Department decided not to bring charges against Mr. Gaetz after concluding it could not make a strong enough case in court. Once the Justice Department inquiry ended, the Ethics Committee resumed its work.

The panel interviewed more than a dozen witnesses, issued 25 subpoenas and reviewed thousands of pages of documents. The committee said in June that it was continuing to investigate the allegations that Mr. Gaetz may have engaged in sexual misconduct and illicit drug use, accepted improper gifts, dispensed special privileges and favors to individuals with whom he had a personal relationship and sought to obstruct government investigations of his conduct.

On Wednesday, Judiciary Committee Democrats wrote to Christopher A. Wray, the F.B.I. director, requesting “the complete evidentiary file” on Mr. Gaetz, including from a Justice Department investigation and the Ethics Committee inquiry, a letter reported earlier by Politico.

Mr. Gaetz has denounced the ethics inquiry as a “political payback exercise” and suggested it was arranged by former Speaker Kevin McCarthy, his bitter rival whose ouster he orchestrated last year.

In a public letter from September, Mr. Gaetz called the Ethics Committee’s work “uncomfortably nosy” and complained that it involved questions about details of his sexual activity.

“The lawful, consensual sexual activities of adults are not the business of Congress,” he wrote.

He noted he had already been investigated by the Justice Department, which opted not to pursue the case.

“The very people who have lied to the Ethics Committee were also lying to them,” he said.

Luke Broadwater and Aishvarya Kavi contributed reporting.

According to the report, the woman, whose name was withheld, told the police that she ended up in Mr. Hegseth’s hotel room after he spoke at the conference in October 2017 hosted by the California Federation of Republican Women at the Hyatt Regency Monterey Hotel and Spa.

The woman, referred to throughout the report as Jane Doe, said Mr. Hegseth took her phone, blocked the hotel room door when she tried to leave, and sexually assaulted her, ejaculating on her stomach. She said her memory was hazy, and that she had drunk far more alcohol than usual throughout the day.

Mr. Hegseth told the police that he repeatedly sought the woman’s consent for sex and told her that they could stop if it was a problem that he did not have a condom. Video footage at the hotel earlier that evening showed them at one point leaving a hotel bar with their arms locked together, the report said.

Mr. Hegseth said that he believed the woman led him to his room, and that he had no plans to have sex with her, the report said. “He might have thought that with someone else, but not Jane Doe,” it said.

The woman’s allegation, the outlines of which surfaced last week, have complicated Mr. Trump’s intention to have Mr. Hegseth lead the Defense Department next year. Mr. Hegseth’s attorney said Sunday that his client had paid the woman an undisclosed amount after she threatened to file a lawsuit against Mr. Hegseth in 2020 simply because he feared he might lose his job as a Fox News anchor if the allegation became public. Mr. Trump has told advisers that he is standing behind Mr. Hegseth, a veteran of the wars in Iraq and Afghanistan.

The Monterey city attorney’s office, released the police report in response to public information requests from news media organizations. The city attorney said that because the report had been released to Mr. Hegseth in March 2021, it was no longer private. The name of the complainant and others interviewed by the police were redacted.

The complaint initially came to the police from a Kaiser Permanente hospital that the woman visited four days after the sexual encounter. The woman went to the hospital to request a sexual assault examination, according to the report.

She told a hospital nurse that she believed that “something” might have been slipped into her drink as she does not remember most of the night’s events, the report said. She said she remembered being in Mr. Hegseth’s hotel room and seeing his dog tags hanging around his neck as he was over her.

The woman could not remember whether intercourse occurred, the nurse’s account said. After Mr. Hegseth ejaculated, the woman said that he told her to “clean it up,” and she found her way back to her hotel room.

Mr. Trump issued the edict in a post on his Truth Social platform Wednesday afternoon. Citing a “PBS NewsHour” report about the federal shield legislation, he wrote: “REPUBLICANS MUST KILL THIS BILL!”

Mr. Trump has exhibited extreme hostility to mainstream news reporters, whom he has often referred to as “enemies of the people.” In his first term as president, he demanded a crackdown on leaks that eventually entailed secretly seizing the private communications of reporters, including some from The New York Times, The Washington Post and CNN.

After those subpoenas came to light early in the Biden administration, Attorney General Merrick B. Garland issued a rule that banned prosecutors from using compulsory legal processes like subpoenas and search warrants to go after reporters’ information — including by asking third parties, like phone and email companies, to turn over their data — or to force them to testify about their sources. But a future administration could rescind that regulation.

The PRESS Act would codify such limits into law.

Trevor Timm, the co-founder and executive director of the Freedom of the Press Foundation, said he hoped Mr. Trump would reconsider, arguing that it would protect all journalists, including those who primarily reach conservative audiences.

“The PRESS Act protects conservative and independent journalists just as much as it does anyone in the mainstream press,” Mr. Timm said. “Democratic administrations abused their powers to spy on journalists many times. The bipartisan PRESS Act will stop government overreach and protect the First Amendment once and for all.”

Mr. Timm cited support for the bill by Republican allies of Mr. Trump like Representative Jim Jordan of Ohio, the House Judiciary Committee chairman, and Senator Mike Lee of Utah, a Senate Judiciary Committee member.

Mr. Timm also noted that Tucker Carlson, the former Fox News host who is influential in Mr. Trump’s circle, endorsed the PRESS Act in an interview with Catherine Herridge, a former Fox News reporter facing fines for contempt of court over her refusal to identify her sources for stories about a scientist who was investigated by the F.B.I. for ties to the Chinese military. The scientist, who was not charged, has sued the government for allegedly disclosing private information about her from the investigation, leading to a subpoena to Ms. Herridge.

The legislation has had broad support across party lines, and passed the House without opposition in January. But it has been stalled in the Senate Judiciary Committee.

The committee, under the leadership of its chairman, Senator Dick Durbin, Democrat of Illinois, has primarily been focused on approving as many of President Biden’s judicial nominees as it can before the session ends and Republicans take over leadership of the chamber next year.

The bill has also run into skepticism from several Republican senators, which makes it harder to bring it up for quick passage or to attach it to some other bill, like the annual defense authorization act.

According to congressional staff, the bill’s primary adversary on the Judiciary Committee has been Senator Tom Cotton of Arkansas, a hawkish Republican who gained public attention as an Army officer in 2006 while serving in Iraq by attacking The New York Times for its publication of an investigative article about a counterterrorism finances program. Another Republican committee member, Senator John Cornyn of Texas, is also said to have expressed some reservations.

Mr. Trump did not give a reason for his abrupt decision to weigh in against the PRESS Act, but some of his other allies have called for rolling back protections for press freedoms.

For example, Project 2025, the consortium of conservative think tanks that devised a detailed governing agenda for Mr. Trump before he won the election, included in the Justice Department chapter of its Mandate for Leadership that a second Trump administration should rescind the Garland regulation.

Kash Patel, a confidant of Mr. Trump, also threatened to target journalists for prosecution in a podcast in December hosted by Stephen K. Bannon, Mr. Trump’s former strategist.

“We will go out and find the conspirators, not just in government but in the media,” Mr. Patel said last year. “Yes, we’re going to come after the people in the media who lied about American citizens, who helped Joe Biden rig presidential elections — we’re going to come after you. Whether it’s criminally or civilly, we’ll figure that out.” He added: “We’re actually going to use the Constitution to prosecute them for crimes they said we have always been guilty of but never have.”

A World War I-era law, the Espionage Act, makes it a crime to solicit or disclose national security secrets without authorization. While the law was written for spies gathering information for a foreign adversary, on its face it also would cover investigative journalism and the publication of information the government has deemed classified.

For most of the century since World War I, however, First Amendment norms kept prosecutors from trying to use that law to treat journalistic-style activities as a crime. But the Trump administration broke that taboo, bringing Espionage Act charges against the WikiLeaks founder Julian Assange for publishing military and diplomatic documents in 2010 that were leaked by Chelsea Manning.

The Biden administration continued that case and won a conviction earlier this year in a plea deal, establishing a precedent that gathering and publishing information the government had deemed secret could be treated as a crime in the United States. For now, that precedent remains ambiguous, however; because Mr. Assange agreed to a deal, there was no appeal to test the constitutional legitimacy of applying the Espionage Act to publishing information.

“If federal employees don’t want to show up, American taxpayers shouldn’t pay them for the Covid-era privilege of staying home,” they wrote.

In their column, Mr. Musk and Mr. Ramaswamy described some of the early aims of the department, which Mr. Trump had said would operate outside of the government and offer input to federal officials. Mr. Musk has promised to eliminate $2 trillion from the annual United States budget, and has said that the government needs only 99 agencies, not more than 400.

Part of the group’s task — cutting down the number of federal regulations — would be providing “sound industrial logic for mass head-count reductions across the federal bureaucracy,” Mr. Musk and Mr. Ramaswamy wrote.

The two men have been advising Mr. Trump’s transition team to hire what they said were “small-government crusaders” to work with the White House’s Office of Management and Budget.

To accomplish the reductions, Mr. Musk and Mr. Ramaswamy wrote, federal appointees working with the efficiency department would identify a minimum number of employees to perform “constitutionally permissible and statutorily mandated functions,” with the number of workers cut proportionate to the number of regulations scrapped.

Mr. Ramaswamy has already outlined his support for five-day workweeks at federal agencies, telling Tucker Carlson recently that such a mandate could lead to a “25 percent thinning out of the federal bureaucracy.”

“You don’t even have to talk about you’re in a mass firing, a mass exodus,” Mr. Ramaswamy said on “The Tucker Carlson Show.” “Just tell them they have to come back five days a week from 8 a.m. to 6 p.m.”

A report issued earlier this year by the Office of Management and Budget found that federal employees who were eligible to work remotely were still spending more than 60 percent of their work hours in offices. Of the 2.3 million civilian workers working for the government in May, the report said, 1.1 million were eligible for telework and about 228,000 were eligible for entirely remote work.

Mr. Trump has promised to reinstitute an executive order he issued late in his term known as Schedule F, which would empower his administration to convert tens of thousands of civil servants to so-called at-will employees, who could more easily be fired. President Biden revoked the order.

“Employees whose positions are eliminated deserve to be treated with respect,” Mr. Musk and Mr. Ramaswamy wrote in The Journal, adding that the efficiency department would “help support their transition into the private sector.”

“The president can use existing laws to give them incentives for early retirement and to make voluntary severance payments to facilitate a graceful exit,” they wrote.

As a political force, however, she has been a “fierce advocate” for transforming the nation’s educational system in a way that Mr. Trump supports, he said when announcing her selection.

Chief among those policies is school choice, meaning that some money that would normally flow to public schools will instead go to families, who can spend it on private education. This was a major push under Mr. Trump’s previous education secretary, Betsy DeVos. Since then, more states have instituted this policy through taxpayer-funded voucher programs.

“As Secretary of Education, Linda will fight tirelessly to expand ‘Choice’ to every State in America, and empower parents to make the best Education decisions for their families,” Mr. Trump said.

Mr. Trump also said Ms. McMahon’s business experience, including as the former chief executive of World Wrestling Entertainment, would help her spearhead an effort to “send Education back to the states” — a reference to one of his key education campaign pledges: to reduce or eliminate the federal Department of Education.

The platform Ms. McMahon has championed as the chair of the board at the America First Policy Institute also supports teaching American history in a more patriotic, less critical way and increasing transparency for parents about what is taught in classrooms. It also backs expanding technical education opportunities and moving away from an emphasis on college for all, a bipartisan push embraced by many in the education world.

On Tuesday, Ms. McMahon posted a message on social media praising “apprenticeship programs” and highlighting examples of them in Switzerland, which is often cited as a high-performing country whose model the United States should follow.

She also has backed a House bill to make federal Pell grants available for those pursuing skills training programs and technical education, not just traditional college degrees.

“Our educational system must offer clear and viable pathways to the American Dream aside from four-year degrees,” she wrote in a column for The Hill in September.

Ms. McMahon’s support of the Pell grant bill was troubling to many advocates of college affordability. The bill would open up the grants to programs that are as short as eight weeks and let the for-profit sector more easily tap federal aid, said Aissa Canchola-Bañez, policy director at the Student Borrower Protection Center. She said she worried it would help “some of the most shady actors in the higher education space.”

For-profit colleges have stirred political conflict. Many Democrats say they have taken advantage of students and of federal money, often posting poor outcomes compared with many of their nonprofit peers. Republicans, including those in the last Trump administration, see the sector, which often operates online, as an important option for students and have championed policies that help it.

The for-profit college sector applauded Ms. McMahon’s selection.

“Under her leadership, we are confident that the new Department of Education will take a more reasoned and thoughtful approach in addressing many of the overreaching and punitive regulations put forth by the Biden administration, especially those targeting career schools,” Jason Altmire, president of Career Education Colleges and Universities, a trade group that represents the for-profit sector, said in a statement.

For universities that faced accusations over the last year that they were allowing antisemitism to go unchecked on their campuses, there are some clues about how she might view the issue.

The America First Policy Institute has said combating campus antisemitism is a major priority, though Ms. McMahon appears not to have personally written about it. Its publications, for example, call for universities to explicitly disavow language some deem antisemitic and for the elimination of diversity, equity and inclusion programming, which the group says has fueled antisemitism because it teaches students to understand the world in terms of victims and oppressors and, the group says, codes Jewish people as oppressors.

Reactions to her nomination from union leaders, public school advocates and some Democrats were fierce and swift.

“By selecting Linda McMahon, Donald Trump is showing that he could not care less about our students’ futures,” Becky Pringle, the president of the National Education Association, said in a statement. She added, “McMahon’s only mission is to eliminate the Department of Education and take away taxpayer dollars from public schools.”

“Donald Trump has chosen yet another unqualified, dangerous sycophant to carry out his agenda,” said Gaylynn Burroughs, vice president of education and workplace justice at the National Women’s Law Center.

But Ms. McMahon’s allies in the area of school choice were delighted.

“Linda is a fierce patriot and a champion for Americans, and I believe that the first thing she can do is empower parents to be in the driver’s seat when it comes to their children’s education,” Tiffany Justice, a co-founder of the parental rights group Moms for Liberty, said in an interview.

She said that in her view, “President Trump has made excellent cabinet choices,” and that by choosing Ms. McMahon, “he is proving that he is dedicated to reclaiming America and getting us back on track.”

Others took a more measured view, saying they looked forward to learning more about her educational views and finding common ground.

Robert C. Scott, the top Democrat on the House Committee on Education and the Workforce, said in a statement that while he was “staunchly opposed to President-elect Trump’s education agenda” he would “wait to pass judgment on her nomination until she has been fully vetted by the Senate.”

Ted Mitchell, the president of the American Council on Education, a higher education association representing all types of colleges and universities, reacted positively to the nomination, saying that Ms. McMahon’s experience in education was stronger than some critics were giving her credit for.

He said that her work as the administrator of the Small Business Administration during Mr. Trump’s first term “connected her to work force development programs in a really important way.” He also singled out her role as a long-serving board member at Sacred Heart University.

“She certainly understands the challenges of running a small college in the current economic environment,” Mr. Mitchell said.

Isabelle Taft , Anemona Hartocollis and Vimal Patel contributed reporting.

What once passed as disqualifying for a presidential nominee seems downright benign in comparison to allegations of sexual misconduct and illicit drug use by his attorney general pick detailed in a secret congressional report, a sexual assault accusation followed by a paid settlement for his choice to head the Pentagon and an acknowledged former heroin addiction by the would-be health secretary.

It was not so long ago that nominees for high-level jobs and even some of the more obscure ones had to be above reproach, to the point where a relatively minor tax issue could derail them. But times are evidently changing when it comes to nominations at the dawn of the second Trump administration.

“Standards are apparently evolving,” said Senator John Cornyn, Republican of Texas and a senior member of the Judiciary Committee. The panel would consider the nomination of former Representative Matt Gaetz, Republican of Florida, for attorney general if he is formally put forward.

Mr. Gaetz was the subject of a Justice Department investigation and a House Ethics Committee inquiry into drug use and whether he had sex with a minor, among other allegations. He and his supporters dismiss the accusations as a smear and emphasize that federal prosecutors declined to charge him, although the underlying claims against him in the case were well documented. The ethics findings remain confidential after the panel deadlocked on Wednesday on whether to release its report.

Senate Democrats are flabbergasted at the accounts surrounding multiple Trump selections for top jobs and contend they would never have gotten past the initial vetting stage of past administrations either Republican or Democrat, let alone be put forward for Senate confirmation.

“That’s stuff you couldn’t get past the vet,” said Senator Michael Bennet, Democrat of Colorado. “Now people wear it like a badge of honor.”

The histories of some of the potential picks have also raised alarm with Republicans who have expressed resistance to Mr. Trump’s selections and the prospect of him making an end run around the Senate confirmation process with appointments while the chamber is in recess.

“I am one who believes that integrity and character matter,” Senator Lisa Murkowski, Republican of Alaska, said in an interview. “I refuse to be deterred, even given some indications that perhaps character and integrity are not the highest qualifications for office.”

Others among her fellow Republicans are untroubled by the histories of the prospective nominees and say that the Senate should quickly consider and approve them or get out of the way, arguing that Mr. Trump is entitled to his personnel preferences.

“There’s a lot of people, if you think about the first Trump administration, that got nominated and never got confirmed,” said Senator Rick Scott, Republican of Florida. “So we’re going to have to figure out, how do we help this president who got elected with a mandate to change the country get his nominations done?”

Senate confirmation has historically been such an arduous process that some potential appointees have declined to go into government rather than face the hearing gantlet and open their lives and finances to intense scrutiny that can uncover potential issues and more.

In previous years, the disclosure of even minor improprieties was often enough to end the nomination process and lead to a withdrawal, sparing the White House and the individual embarrassment before the nomination got to a vote. It is rare that a cabinet nominee is actually defeated. The last was in 1989, when former Senator John Tower, Republican of Texas, made it all the way to the floor only to be rejected as defense secretary by the Democratic-controlled Senate because of alcohol abuse and other issues.

But Mr. Trump, who has faced his own accusations of sexual abuse and election subversion, does not appear embarrassed in the least about the backgrounds of his choices and has so far shown no inclination to back down on them. Instead, he has doubled down as is his habit, giving them full-throated endorsement as the kind of people who will enact the change he demands.

It is a difference from the past. Take Tom Daschle, the former Senate Democratic leader whom President Barack Obama nominated in 2008 to be health secretary. It was discovered that he never paid income taxes on the use of a car and driver lent to him while he consulted for a financial firm. Mr. Daschle said he was unaware that the car counted as income, and he paid more than $100,000 in back taxes. But the damage was done, and it was determined he couldn’t clear the Senate he once led.

Not one but two of President Bill Clinton’s potential attorney general selections were found to be objectionable because of their employment of undocumented immigrants and, in the case of the corporate lawyer Zoe Baird, failing to pay the required payroll taxes for them. After that, “nanny tax” issues became a standard vetting question for prospective presidential picks. Other potential nominees for a variety of posts ended up withdrawing because of tax liens or questions about their deductions.

In another high-profile incident, Judge Douglas H. Ginsburg was forced to withdraw his name from consideration as President Ronald Reagan’s nominee for a Supreme Court vacancy in 1987 after it was disclosed that he had smoked marijuana as a college student in the 1960s and occasionally again in the 1970s while on the faculty at Harvard Law School.

Robert F. Kennedy Jr., Mr. Trump’s pick for health secretary, has acknowledged a yearslong addiction to heroin. He was convicted of possessing heroin after his arrest following a flight to South Dakota in 1983 and says he has been in recovery since then.

As for the tweets, Neera Tanden, President Biden’s nominee to lead the Office of Management and Budget, withdrew after it was determined that she couldn’t clear the narrowly divided Senate in 2021 because of previous social media posts critical of senators. Mr. Gaetz’s social media feed is replete with digs at some of the same senators whose votes he now needs to be confirmed, but there appears to be no move to withdraw him.

Both Democrats and Republicans have also expressed concern about reports that Pete Hegseth, an Army veteran and Fox News personality whom Mr. Trump has tapped for defense secretary, reached a settlement to avoid a lawsuit by a woman who accused him of sexual assault at a 2017 conservative conference in California.

Democrats say the questions about the Trump picks go beyond the minor infractions on the records of past nominees who didn’t pass muster.

“These aren’t blemishes,” said Senator Chris Coons, Democrat of Delaware. “These are deep stains.”

He and others said the rationale that criminal charges weren’t filed in some cases — as was the case for both Mr. Gaetz and Mr. Hegseth — does not meet the traditional confirmation standard.

“In the past, this sordid, raunchy, indisputed involvement in criminality would have been totally disqualifying,” said Senator Richard Blumenthal, Democrat of Connecticut and another member of the Judiciary Committee.

Mr. Cornyn, the Texas Republican, said the questions surrounding nominees and their backgrounds demonstrated why the Senate must follow its traditional confirmation process to sort out which reports are true or not. He has pressed for the release of the House Ethics Committee’s report on Mr. Gaetz, for instance, and even said he would be open to issuing a subpoena if the panel refused to allow senators to see it.

“I have no idea whether it’s people’s speculation or it’s factual or it’s opinion,” he said of the allegations against the prospective nominees. “That’s why the best thing we can do is just do our due diligence.”

On Wednesday, Mr. Vance, now the vice president-elect, returned with considerably more political capital, but also significant questions about whether it was enough to persuade his erstwhile colleagues to confirm Mr. Gaetz as the nation’s top law enforcement officer.

The two men, who have campaigned together before, hunkered down for much of the day in the Strom Thurmond Room in the Capitol, an ornate conference room just steps from the Senate floor, as senators streamed in individually and in pairs.

At the same time, the allegations against Mr. Gaetz were coming into sharper focus. Federal investigators established a trail of payments from Mr. Gaetz to women, including some who testified that Mr. Gaetz hired them for sex, according to a document obtained by The New York Times and a lawyer representing some of the women. He has denied their accounts, and the federal investigation was closed by the Justice Department without any charges against him.

But behind closed doors on Capitol Hill, Mr. Vance and Mr. Gaetz asked senators to keep an open mind. According to people who met with them, they asked the senators to allow Mr. Gaetz to defend himself and hear his plans for overseeing more than 10,000 attorneys in the world’s largest law firm, known as the U.S. Department of Justice.

In a social media post on Wednesday, Mr. Vance offered a glimpse of the message he delivered during the meetings, crediting Mr. Trump’s victory with carrying Republicans to the majority in the Senate.

“He deserves a cabinet that is loyal to the agenda he was elected to implement,” Mr. Vance said.

How much progress the two men made was unclear.

“We didn’t get into a lot of details,” Senator Mike Lee of Utah said. “But he expressed confidence that what is before the committee are a series of false accusations.”

The meetings focused on Republican members of the Senate Judiciary Committee, which will be the first stop for Mr. Gaetz once Mr. Trump takes office in January. Most senators said after their meeting that Mr. Gaetz deserved a fair hearing, even while acknowledging there was little discussion about specific allegations.

Senator Lindsey Graham of South Carolina, the top Republican on the judiciary panel, was the first to meet with the pair. He said he told Mr. Vance and Mr. Gaetz that there would be “no rubber stamps and no lynch mob.”

“Matt is a very, very smart guy,” Mr. Graham told reporters. “These allegations will be dealt with in committee, but he deserves a chance to confront his accusers.”

Most of the meetings lasted about 45 minutes. One of the quickest discussions was with Senator John Cornyn, Republican of Texas, whose visit lasted for about 20 minutes. He said it was the first time he had met Mr. Gaetz, a combative Floridian known for his fierce loyalty to Mr. Trump and his willingness to agitate fellow Republicans.

“It’s a beginning,” Mr. Cornyn said about their conversation. “We’re going to do our investigations and our research and give him the opportunity to answer any questions.”

Senator Josh Hawley of Missouri said Mr. Gaetz wanted the chance to show how he would ensure that the Justice Department was not engaged in “politically motivated, partisan activity.”

Mr. Trump spent much of his presidential campaign complaining, without proof, that the criminal charges he faced were designed to keep him out of the White House while also vowing to seek retribution by targeting his political opponents.

“We’ve got to remember that a cabinet secretary is not an exercise in individuality,” Mr. Hawley said. “You’re there to serve the president, and he has a sense of what the president wants to do in terms of prioritizing law enforcement.”

Republican senators have expressed alarm about the selection of Mr. Gaetz, whose resignation from the House last week effectively ended the yearslong investigation by the House Ethics Committee into the sexual misconduct allegations. On Wednesday, Republicans on the committee blocked the release of a report into those allegations.

Mr. Trump has remained unequivocal about his selection of Mr. Gaetz and has assigned his running mate the task of shepherding him and other embattled nominees through the initial stages of their confirmation process. That task is not typically carried out by the vice president-elect; usually it is a job for a midlevel official or someone with deep personal relationships on the Hill.

Mr. Vance will get another chance on Thursday, when he is scheduled to host similar meetings for Pete Hegseth, the Fox News host Mr. Trump has picked for defense secretary. Mr. Hegseth, a veteran of the wars in Iraq and Afghanistan, is facing allegations that he sexually assaulted a woman, which he has denied.

A correction was made on

Nov. 20, 2024

:

Because of an editing error, an earlier version of this article referred incorrectly to the timing of Pete Hegseth’s visit to Capitol Hill. His appearance was moved to Thursday; he was not there on Wednesday, as previously expected.

When we learn of a mistake, we acknowledge it with a correction. If you spot an error, please let us know at nytnews@nytimes.com.Learn more