WASHINGTON — 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 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.

Trump 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 FBI made up evidence against Trump, left the team 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. Trump had also considered hiring diGenova’s wife, Victoria Toensing, but she will also not join the team.

That leaves the president with just one personal lawyer working full time on the special counsel’s investigation as 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. 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 diGenova’s departure, which 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 veteran lawyer Emmet Flood about the possibility of joining the legal team. But Trump was put off by the fact that Flood, a Republican, had represented Bill Clinton during his impeachment process, and 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.

Trump also tried to recruit Ted Olsen, a well-known Republican lawyer, but Olsen has said he would not be representing the president.

The first phase of legal work for Trump in the inquiry by the special counsel, Robert Mueller, 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 Mueller, had been led by Dowd. One reason Dowd quit was that, against his advice, Trump was insistent that he wanted to answer questions under oath from Mueller, believing it would help clear him.

Dowd had concluded that there was no upside and that the president, who often does not tell the truth, could increase his legal exposure if his answers were not accurate.

Roger Cossack, a seasoned legal analyst, said the key to successfully defending a high-profile client under immense scrutiny was to have a cohesive legal team with a consistent strategy.

“In these types of cases, you need highly competent lawyers and a client who will listen and follow their advice,” Cossack said. “If you don’t have both, you have what we’re seeing here: chaos and disaster.

“You have a client who clearly thinks he has a better idea of how things should work than the lawyers who, from time to time, have told him things he doesn’t want to hear,” he added. “He is looking for the guy who can say, ‘I know how to handle Mueller, I know you think he is bad, and we’ll take care of it.’ Problem is you can’t find that lawyer because no one will be able to do that.”

People close to Trump say the upheaval in the legal team was inevitable. When Kasowitz took the lead after Mueller was appointed in May, he wanted to follow a model used by Clinton, with a separate team of lawyers and communications professionals handling issues related to the inquiry, so the White House staff could keep its distance.

But Trump, who trusts few people and considers himself his best lawyer, spokesman, and strategist, never wanted that type of system. As a result, his legal and public relations strategies have been out of sync, with the president at times publicly contradicting his lawyers, and the White House often finding itself flat-footed in the face of new disclosures about the Russia investigation.

The president’s decision has also exposed many of his aides, leaving them deeply enmeshed in an inquiry that is likely to cost them tens of thousands of dollars in legal fees.

But while Trump has struggled to find lawyers, his family and his close associates are being represented by some of the country’s top legal talent.

His son-in-law, Jared Kushner, has hired Abbe Lowell, a longtime Washington lawyer who recently got the Justice Department to drop corruption charges against US Senator Robert Menendez, Democrat of New Jersey, after a lengthy court fight.

Three prominent current and former White House officials — the former chief strategist, Stephen K. Bannon; the former chief of staff, Reince Priebus; and the White House counsel, Donald F. McGahn — are being represented by William A. Burck, who turned down the chance to represent the president but has worked for high-profile witnesses in federal investigations, including Maureen McDonnell, the wife of a former Virginia governor.

The turmoil in Trump’s legal team started within weeks of the appointment of Mueller. Kasowitz pushed for an adversarial approach to the special counsel, which the president was poised to follow. But Kasowitz clashed with Kushner, and he was soon pushed aside after a series of missteps and embarrassing incidents.

The president then hired Cobb, a veteran Washington lawyer, to lead efforts within the White House, as well as Dowd, who was put in charge of his personal legal team. They advocated a strategy of cooperation, telling the president that the sooner he gave Mueller’s office what it wanted, the sooner his name would be cleared.

While Cobb had told the president that the investigation would be over by now, it seems to be accelerating. Mueller is still looking into a wide range of matters related to Trump’s corporate activities, his 2016 campaign, his associates and his time in office.

Trump, hoping to bolster his team, met with diGenova and Toensing in recent days but, according to two people told of details about the meeting, did not believe he had personal chemistry with them.

There were also significant conflict-of-interest issues, but Trump could have waived them if he wanted. Toensing is representing Mark Corallo, who was the spokesman for Trump’s legal team in 2017 before they parted ways. Corallo has told investigators that he was concerned that a close aide to Trump, Hope Hicks, may have been planning to obstruct justice during the drafting of a statement about a meeting between a Russian lawyer and Donald Trump Jr. during the campaign.

Hicks’ lawyer has strongly denied that suggestion, and White House aides said Corallo’s assertion had come up in discussions with the president as he weighed whether to go ahead with diGenova and Toensing.

DiGenova had been expected to serve as an outspoken voice for the president as Trump has increased his attacks on Mueller. DiGenova has endorsed the notion that a secretive group of FBI agents concocted the Russia investigation as a way to keep Trump from becoming president, a theory with little supporting evidence.