WASHINGTON — President-elect Donald Trump’s pick for Defense Secretary Pete Hegseth spent a second day Tuesday on Capitol Hill, meeting privately with Republican senators amid rising questions about his ability to effectively lead the Pentagon.

Hegseth told reporters he was planning to sit down with senators, even with those potentially skeptical of his nomination.

“We’re gonna meet with every senator that wants to meet with us, across the board,” Hegseth as he went from office to office Tuesday. “And we welcome their advice as we go through the advice and counsel process.”

Trump tapped the Fox News co-host, who had served in the Army National Guard, as his Secretary of Defense, typically among the first Cabinet posts to be considered by the U.S. Senate for confirmation.

But Hegseth is running into questions amid a sexual assault allegation, which he has denied, and other emerging reports about his work conduct and history.

GOP Sen. Lindsey Graham said some of the reports are “disturbing.”

“I want to make sure that every young woman that joins the military feels respected and welcomed,” Graham told CBS News.

The South Carolina lawmaker told the AP later that he doesn’t know whether to believe the allegations, and Hegseth “has a chance to say that’s true or not true.”

Sen. Josh Hawley, R-Mo., said he’s seen the reports. “I’ll get the chance to talk to him, and I’m sure he’ll address them,” he said. “But my view is, have the hearing.”

Trump is drawing from the ranks of loyalists to fill his administration and to Cabinet positions, often stunning Washington with unusual choices that are provocative and testing the senators who will be asked to confirm them under the chamber’s advise and consent role.

An early pick, Matt Gaetz, the former congressman from Florida, abruptly withdrew from consideration when it became clear that Senate support was crumbling. Gaetz, who had been investigated but never charged in a federal sex trafficking probe, faced a House Ethics investigation over sexual misconduct.

Trump’s choices can only afford to lose a few detractors in the Senate, where it takes majority approval to be confirmed. Republicans will have a 53-seat majority in the new year, meaning four GOP votes could sink a nominee, if all Democrats are opposed.

Republican senators have been weighing their options. There have been private discussions among senators about the allegations and how to approach the situation, according to one person granted anonymity to discuss the private conversations.

During a closed-door meeting with about a dozen senators late Monday evening, none asked Hegseth about the allegations against him.

“You know what? The American people care about restoring our military,” said Sen. Ted Cruz, R-Texas, after the meeting. He decried as “shameful” the criticism of Hegseth.

While Republican senators are reluctant to raise questions publicly — and several dismissed the reports outright — many of them indicated he could face tough questions in a confirmation hearing.

“That’s what the process is for,” said Utah Rep. John Curtis, an incoming freshman senator.

Questions about Hegseth and other nominees are “why a background check is important, why a committee investigation is critical,” said Maine Sen. Susan Collins.

Alabama Sen. Tommy Tuberville said after meeting Monday with Hegseth that he is very supportive of the nomination.

But Tuberville said of the allegations: “If it’s to a certain degree, people aren’t going to vote to confirm him.”

Hegseth, 44, was a co-host of Fox News Channel’s “Fox and Friends Weekend” and had been a contributor with the network since 2014. He developed a friendship with Trump, who made regular appearances on the show.