Jay Sekulow is the only personal lawyer for President Trump who is working full time on the special counsel’s investigation as Mr. Trump faces a significant decision: whether to sit for an interview.

As President Trump heads into one of the most critical phases of the special counsel’s investigation, his personal legal team has shrunk to essentially just one member, and he is struggling to find any top lawyers willing to represent him.

Working for a president is usually seen as a dream job. But leading white-collar lawyers in Washington and New York have repeatedly spurned overtures to take over the defense of Mr. Trump, a mercurial client who often ignores his advisers’ guidance. In some cases, lawyers’ firms have blocked any talks, fearing a backlash that would hurt business.

The president lost two lawyers in just the past four days, including one who had been on board for less than a week.

Joseph diGenova, a longtime Washington lawyer who has pushed theories on Fox News that the F.B.I. made up evidence against Mr. Trump, left the team on Sunday. He had been hired last Monday, three days before the head of the president’s personal legal team, John Dowd, quit after determining that the president was not listening to his advice. Mr. Trump had also considered hiring Mr. diGenova’s wife, Victoria Toensing, but she will also not join the team.

That leaves the president with just one personal lawyer who is working full time on the special counsel’s investigation as Mr. Trump is facing one of the most significant decisions related to it: whether to sit for an interview.

That lawyer, Jay Sekulow, is a conservative commentator who made his name on religious freedom cases. Mr. Sekulow is in talks with other lawyers about joining the team, although it is not clear how far those discussions have progressed.

Hours before the announcement of Mr. diGenova’s departure, which Mr. Sekulow said was related to a conflict of interest, the president took to Twitter to reject any suggestion that lawyers do not want to work for him.

“Many lawyers and top law firms want to represent me in the Russia case … don’t believe the Fake News narrative that it is hard to find a lawyer who wants to take this on,” he wrote. “Fame & fortune will NEVER be turned down by a lawyer, though some are conflicted.”

Adding new lawyers, he said, would be costly because they would take months “to get up to speed (if for no other reason than they can bill more).”

“I am very happy with my existing team,” he added.

This month, the president met with the veteran lawyer Emmet Flood about the possibility of joining the legal team. But Mr. Trump was put off by the fact that Mr. Flood, a Republican, had represented Bill Clinton during his impeachment process, and Mr. Flood has made clear that he will not represent the president if Marc E. Kasowitz, his brash longtime personal lawyer, has any role in the effort.

Mr. Trump also tried to recruit Theodore B. Olson, a well-known Republican lawyer, but Mr. Olson has said he would not be representing the president.

The first phase of legal work for Mr. Trump in the inquiry by the special counsel, Robert S. Mueller III, was led by a White House lawyer, Ty Cobb. That work, which in part involved the production of documents and the arrangement of interviews with White House officials, has been largely completed.

The second phase, which is now focused on the question of a presidential interview with Mr. Mueller, had been led by Mr. Dowd. One reason Mr….