By Katelyn Polantz, CNN

(CNN) -- Several top US law firms have left President Donald Trump with few places to turn for legal help in the Russia probe.

Five large law firms are passing on the opportunity to represent the President after a shakeup last week on his private defense team and as he anticipates giving possible testimony to special counsel Robert Mueller's investigation.

Well-known Washington lawyers cited several reasons for declining the President in recent weeks, according to multiple sources familiar with their decisions. Among them, Trump appears to be a difficult client and has rebuked some of his lawyers' advice. He's perceived as so politically unpopular he may damage reputations rather than boost them. Lawyers at large firms fear backlash from their corporate clients if they were to represent the President. And many want to steer clear of conflicts of interest that could complicate their other obligations.

"With a figure who is as polarizing as the President, it makes the decision about whether to represent him a more difficult one," said Philip West, chairman of large Washington law firm Steptoe & Johnson. The firm was among several to decline to represent Trump last year. "Any large law firm has clients that have very strong feelings."

Even in a city with such a sizable legal industry, so many top lawyers and large law offices with white-collar and national security specialists have already been hired by witnesses, subjects and companies involved in the Mueller probe. Thus, few in town can take new clients at the center of it.

The result is a previously unheard-of Washington problem: The President of the United States is struggling to build an experienced, large legal defense team as the special prosecutor digs in to his campaign and administration. His official legal defense team consists of two lawyers, Ty Cobb and Jay Sekulow, neither affiliated with a traditional law firm.

The latest to turn down the invitation, Dan Webb and Tom Buchanan of the law firm Winston & Strawn, said Tuesday they "were unable to take on the representation due to business conflicts." Webb and others at the firm represent the Ukrainian oligarch Dmytro Firtash in a criminal money laundering case in Chicago, where he continues to face possible extradition from Austria. Firtash was previously a business contact of indicted former Trump campaign chairman Paul Manafort, making the Ukrainian potentially connected to the Mueller probe.

"However they consider the opportunity to represent the President to be the highest honor and they sincerely regret that they cannot do so," Webb and Buchanan's statement said. "They wish the President the best and believe he has excellent representation in Ty Cobb and Jay Sekulow."

While Sekulow, the leader of a non-profit religious advocacy legal group and a talk radio personality, is Trump's sole remaining private defense counsel, Cobb works within the White House as a special counsel overseeing the Russia probe response.

When asked who would lead Trump's legal defense team on Tuesday, White House press secretary Sarah Sanders said that "the President has a highly qualified team." She referred further questions to Sekulow.

Other lawyers who received recent requests to help with the Russia probe include former US Solicitor General Ted Olson; Emmet Flood, who's worked for multiple presidents and still may join the White House counsel's office; Robert Bennett, Bill Clinton's attorney in the Paula Jones litigation; and Bob Giuffra, a New York litigator with the high-end firm Sullivan & Cromwell.

Olson, Bennett and Giuffra all said no shortly after they were asked. The invitations became public last week when John Dowd, Trump's private attorney for Mueller matters, quit. Dowd, who previously worked for a large firm and handled several high-profile trials, was central to determining Trump's legal strategy and negotiating with Mueller's office. Trump then failed last week to bring aboard a husband-and-wife replacement team to aid Sekulow, after announcing that Joe DiGenova and Victoria Toensing would join his team. Sekulow cited conflicts as the problem.

A source familiar with the White House said other lawyers in Washington and New York have reached out to help and could still join the team. The person would not name those lawyers, or explain the timeline.

Earlier this week, Bennett told Politico he hoped Cobb would leave the White House. "He's not helping himself or his reputation," Bennett said.

Olson said on MSNBC on Monday that Trump's White House is in "chaos" and "beyond normal." Olson declined to speculate on what kind of legal help Trump may still need.

Ted Boutrous, another top partner at Olson's firm, said Gibson, Dunn & Crutcher almost immediately declined to represent the President. Boutrous counsels Fusion GPS in court cases over the so-called dossier of Trump opposition research it funded. He wouldn't speak about his law firm's thinking in declining Trump, but pointed out how lawyers can't take on clients when other clients' interests might conflict. The firm also handled Facebook's response to Mueller in recent months.

Boutrous added the President is a "notoriously difficult client who disregards the advice of his lawyers and asks them to engage in questionable activities."

(Another personal attorney to Trump, Michael Cohen, is caught in a legal fight over a nondisclosure agreement made on Trump's behalf with the porn star Stormy Daniels.)

Among the lawyers Trump has considered on Russia issues, Flood still may be willing to work alongside the President. He is a candidate for a position in the Trump White House counsel's office, which handles official White House legal questions, such as the selection of judges and reviewing policy proposals.

This isn't the first time well-known attorneys declined to help Trump against Mueller. Several who were asked this year were also approached last year. Flood, Giuffra, Olson plus three others said no. Those lawyers were William Burck, who now counsels Reince Priebus, Steve Bannon and White House counsel Donald McGahn as Mueller witnesses; attorneys from the law firm Kirkland & Ellis; and trial lawyer Reid Weingarten of Steptoe & Johnson.

Even so, Trump continues to receive legal advice from several commentators and longtime confidants. Marc Kasowitz continues to speak with the President regularly, for instance. Kasowitz's law firm in New York, which advised Trump to push back against Mueller publicly early on, took a diminished role on the team months ago.

The President has also tweeted in support of the legal punditry of Harvard Law Professor Alan Dershowitz, who has criticized Mueller. Dershowitz said he's uninterested in officially joining the team.

Trump has a few other large law firms and well-known lawyers still in his orbit. They handle everything from lawsuits to his taxes. Aside from the White House counsel's office, those lawyers include Charles Harder, who is defending Trump in his Stormy Daniels litigation; the law firm Jones Day, which defends the Trump campaign in court; the Republican campaign finance expert and trial lawyer Bobby Burchfield, acting as an independent ethics adviser for the Trump family business interests; and the law firm Morgan, Lewis & Bockius, which set up a trust for Trump's business assets last year.