Vice President-elect JD Vance was on Capitol Hill on Wednesday to usher Matt Gaetz, one of Donald J. Trump’s most embattled Cabinet picks, to meetings with key senators. It amounts to the highest profile public assignment for Mr. Trump’s heir apparent since the president-elect won the White House earlier this month.

Mr. Vance shepherded Mr. Gaetz, the former representative from Florida who is Mr. Trump’s pick to be the nation’s next attorney general. On Thursday, he’s expected to do the same for Pete Hegseth, the Fox News host who is up for secretary of defense. Both men are under fire for past allegations of sexual misconduct.

Even Republican senators have expressed alarm about the selection of Mr. Gaetz, whose resignation from the House last week effectively ended a yearslong investigation by the House Ethics Committee into accusations that he engaged in sexual misconduct and illicit drug use.

Senator Lindsey Graham, Republican of South Carolina, said he met with Mr. Vance and Mr. Gaetz and told them there would be “no rubber stamps, no lynch mobs” in the confirmation process. “These allegations will be dealt with in committee, but he deserves a chance to confront his accusers,” Graham told reporters.

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 co-host of a weekend Fox News program, he also faces questions about his ability to serve as the incoming president’s principal adviser on defense policy while leading an agency overseeing 750 military bases worldwide. Mr. Hegseth’s meetings with senators had been scheduled for Wednesday before being pushed back a day.

But Mr. Trump has remained unequivocal about his choices and has assigned his running mate, a senator from Ohio, the task of shepherding them 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.

Thank you for your patience while we verify access. If you are in Reader mode please exit and log into your Times account, or subscribe for all of The Times.

Thank you for your patience while we verify access.

Already a subscriber? Log in.

Want all of The Times? Subscribe.