WASHINGTON — Alaska's senior Republican Sen. Lisa Murkowski is once again on the radar of those advocating against one of President Donald Trump's Cabinet nominees — this time for the man who is in line to be labor secretary.

Murkowski is one of four Republican members of the Health, Education, Labor and Pensions Committee who have so far withheld their full support for Andrew Puzder's nomination to head the U.S. Department of Labor. The committee will hold a confirmation hearing Thursday, where he will likely face questions about a range of accusations that have given some lawmakers pause.

Other senators withholding immediate support are Susan Collins, R-Maine, Johnny Isakson, R-Ga., and Tim Scott, R-S.C.

"Well I don't know that I would consider it a swing vote," Murkowski said Tuesday. But she said she plans to consider "the things that I have heard and discussed with him, and will factor in the upcoming hearing on Thursday and take that all into account" before making a decision.

There are several issues at play: Puzder revealed he previously employed an undocumented immigrant as a housekeeper. The fast food executive has faced numerous wage violation complaints at his restaurants and strenuously opposes raising the minimum wage.

And Puzder has faced criticism for the sexually suggestive ads commonly used by one of his companies. Puzder is CEO of CKE Restaurants, parent company of Hardee's and Carl's Jr.

But one key issue nagging some senators is more personal than political: Puzder's ex-wife appeared on the "Oprah Winfrey Show" in the 1980s, in disguise, and claimed her husband had physically assaulted her. Murkowski said she has seen the tape, which was provided to senators on the committee vetting Puzder's nomination.

Since then, Puzder's ex-wife, Lisa Fierstein, has retracted the allegations.

Murkowski notably announced she would not vote for President Donald Trump in 2016 after allegations of sexual assault and the release of an audiotape where Trump described his own activities in lewd terms.

But she said Tuesday she hasn't quite decided what to make of the allegations — and retraction — by Puzder and his ex-wife.

"It's factoring into the questions and the issues that have been raised," Murkowski said. She said she spoke to Puzder about the issue in person, during their first private sit-down. "He raised it with me," she said, noting she appreciated that.

"So, we had an opportunity to discuss it. He has made available to me as well as all of the other committee members, the letter from his former wife recanting everything, and her contact has been made available to us in the event that we wish to speak directly with her," she said.

Murkowski said it is difficult to know where to draw the line on "a personal issue between two people from years ago."

But for now, she's talking to Alaskans and asking for input on Puzder's nomination, she said.

Last week, the head of Alaska's Cabaret, Hotel, Restaurant & Retailers Association wrote Murkowski to support Puzder's nomination, saying he has been an industry leader and "an effective advocate for American business." The National Retail Federation has also urged the Senate to confirm Puzder.

Murkowski and Collins nearly cost Education Secretary Betsy DeVos her position when they crossed party lines last week to vote against her. In an unprecedented move, Vice President Mike Pence was called in to break a tie on a confirmation vote.

Senate rules require only a simple majority to confirm a president's Cabinet nomination. Republicans hold a slim 52-48 majority, so it takes just three Republicans to throw a party-line vote into jeopardy.

Murkowski and other lawmakers were flooded with calls in the lead-up to the DeVos vote.

Since then, calls have continued to come in "nonstop," Murkowski said, noting her office had redesigned her voicemail system to take more messages, and relieve the pressure on the two front-desk staffers. A wider variety of staff now downloads, listens to and logs voicemail messages, she said.

Murkowski answered the phone herself on Friday for 45 minutes, she said. Callers wanted to talk about DeVos, Puzder, Environmental Protection Agency nominee Scott Pruitt and climate change, she said. But "most of it was nominees."

On Tuesday, most of the calls were about Puzder, a staffer whispered to Murkowski while taking a call.

Asked if those callers were opposed to his nomination, she said: "I'm assuming so. They usually are."

On Tuesday, the Alaska Democratic Party sent out an email urging supporters to "make sure Senator Murkowski hears from us" about Puzder's nomination.

And Hart Research, a polling firm, operated a "push poll" in Alaska over the weekend, sharing negative views on Puzder in questions asked of 400 Alaskans on behalf of the National Employment Law Project.

The poll, which found opposition to Puzder's nomination in the state, was meant to urge Murkowski to vote no on his nomination.

"If Puzder's past history is any indication, he will use the role of labor secretary to bolster his low-wage-industry CEO buddies, instead of the workers who helped him build millions in profits," said Christine Owens, NELP executive director.