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

“We’re going to 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, a former Army National Guard major and combat veteran who deployed to both Iraq and Afghanistan, 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.”

Before he was tapped to serve as a weekend host of “Fox & Friends,” Hegseth served at two veterans advocacy groups, Concerned Veterans for America and Veterans For Freedom.

In new allegations this week, the New Yorker cited what it described as a whistleblower report and other documents about his time leading CVA that alleged multiple incidents of alcohol intoxication at work events, inappropriate behavior around female staffers and financial mismanagement.

NBC News reported that several unnamed current and former Fox employees who worked with Hegseth that his drinking habits raised concerns, including some who said he would show up smelling of alcohol.

The Associated Press spoke to four people who had either worked at CVA or were familiar with Hegseth’s time there who insisted on anonymity because they were not allowed to speak to the media or had signed nondisclosure agreements.

While the group’s all-day conferences could run late and often wind up at a nearby bar, three of the four said they had not seen Hegseth intoxicated at events.

One person who had been connected to CVA told the AP, however, that some employees had raised concerns about Hegseth’s alcohol use but said that his departure from the group was more connected to growing ideological differences between him and the network of conservative nonprofits funded by billionaire donors Charles Koch and his late brother, David Koch.

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.

If confirmed, Hegseth would not only be part of critical command and control of the nation’s nuclear weapons, he would be sixth in the line of succession to the presidency. It’s a position that ages its occupants and demands constant response, due to the number of middle-of-the-night contingencies that can occur when U.S. service members are put in harm’s way.

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.

Hegseth served in the Army National Guard from 2002 to 2021, deploying to Iraq in 2005 and Afghanistan in 2011 and earning two Bronze Stars. He lacks senior military and national security experience and would oversee global crises ranging from Europe to the Middle East.

A woman told police that she was sexually assaulted in 2017 by Hegseth after he took her phone, blocked the door to a California hotel room and refused to let her leave, according to a detailed investigative report recently made public.

Hegseth told police at the time that the encounter had been consensual and has denied any wrongdoing.