Pete Hegseth, President-elect Donald Trump's pick for defense secretary, said on Wednesday he will not "back down" after new misconduct allegations have caused growing concern among Republican senators who would vote on whether to confirm him.

"I'm doing this for the warfighters, not the warmongers. The Left is afraid of disrupters and change agents. They are afraid of @realDonaldTrump -- and me. So they smear w/ fake, anonymous sources & BS stories. They don't want truth. Our warriors never back down, & neither will I," Hegseth wrote on X.

As he arrived on Capitol Hill on Wednesday for another day of meetings with Republican lawmakers, Hegseth said he spoke briefly with Trump earlier that morning.

"He said keep going, keep fighting. I'm behind you all the way," Hegseth told CBS News.

Asked if he's committed to remaining in the running, Hegseth replied, "Why would I back down? I've always been a fighter. I'm here for the war fighters. This is personal and passionate for me."

His comments come as a number of senators have privately signaled that they are not inclined to vote to confirm Hegseth as Trump's next defense secretary, leading Trump's advisers to begin discussing who may be a viable replacement, sources familiar with the matter told ABC News.

Sources told ABC News that at least six senators have privately indicated that they don't intend to support Hegseth amid the growing allegations, including about mistreatment of women.

Multiple sources also tell ABC News that Trump and Florida GOP Gov. Ron DeSantis spoke about the job Tuesday and DeSantis expressed interest in it.

Hegseth is due to meet with Ernst on Wednesday afternoon.

His mother, Penelope Hegseth, offered a defense of her son on "Fox and Friends" on Wednesday morning.

Hegseth's mother sent an email to her son in 2018 amid his divorce in which she wrote that he was an "abuser of women." The email was reported by the New York Times. ABC News has not independently obtained the email.

Penelope Hegseth on Wednesday said her son was a "changed" man and that the email was written in "haste" during a "very emotional time." She said that she "retracted it with an apology email" just hours after she sent it, and that her and her son are "very close today."

She also noted the allegations against Hegseth were from several years ago and claimed "most of it" is "misinformation" -- while repeatedly stressing that her son is a now different man who has been "redeemed" and "forgiven."

"We really believe that he is not that man he was seven years ago. I'm not that mother, and I hope people will hear that story today and the truth of that story," she said.

The New Yorker, citing what it called a detailed seven-page whistleblower report, said Hegseth was forced to step down from two veteran nonprofit groups amid accusations of financial mismanagement, sexist behavior and other disqualifying conduct. ABC News has not independently confirmed the magazine's account.

Several Republican senators on Tuesday said they believed Hegseth needed to come forward and address the reports, which Sen. Lindsey Graham called "disturbing." But as he made his way through the Capitol to try to shore up support to lead the Defense Department, he ignored reporters' questions.

Penelope Hegseth said on Fox News that she believed her son was "the man for the job."

ABC News' Rick Klein and Rachel Scott contributed to this report.