Hegseth’s Support With Trump Teeters as He Faces a Series of Critical Tests

President-elect Donald J. Trump’s support for Pete Hegseth, who he announced as his nominee for defense secretary shortly after Election Day, is wobbling after a crush of controversy over a rape allegation and a 2018 email from Mr. Hegseth’s mother accusing him of a pattern of abuse toward women.

How Mr. Hegseth fares through a series of tests on Wednesday will be critical for his chances. He is set to meet with key senators, including Joni Ernst of Iowa, a combat veteran who has spoken about being sexually assaulted herself, and his mother is expected to sit for an interview on Fox News. He is also set to start defending himself on television.

Mr. Trump has made clear to people close to him that he believes Mr. Hegseth should have been more forthcoming about the problems he would face getting confirmed, according to two people with knowledge of his thinking.

The combination of events could determine whether he hangs on as the expected nominee. Mr. Trump is openly discussing other people for the job, including Gov. Ron DeSantis of Florida, whom he defeated in the Republican presidential primaries and with whom he has had a contentious relationship. Mr. Trump likes the story of bringing on someone he dominated publicly, and he talked about it with Mr. DeSantis yesterday at a service honoring three Florida sheriff’s deputies who were killed in a car crash.

But the number of people in Mr. Trump’s world who dislike and distrust Mr. DeSantis — and bitterly recall the campaign he ran against the president-elect — is vast. Those people are discussing other options, including whether Mike Waltz, the Florida congressman who Mr. Trump picked as his national security adviser, could slide into the job, expecting he would be confirmed fairly easily by the Senate. While criticizing Mr. Trump in the past is not always an obstacle for his appointees, Mr. DeSantis threw aggressive jabs at Mr. Trump during the primary. They included a flip line about paying money to a porn star, which was the basis for an indictment against Mr. Trump.

“I think some of these articles are very disturbing,” Senator Lindsey Graham of South Carolina, a close Trump ally, told CBS News, referring to Mr. Hegseth. “He obviously has a chance to defend himself here, but some of this stuff is going to be difficult.”