President Trump’s effort to hire new defense lawyers in the Russia investigation had faltered badly when he met at ­Mar-a-Lago this month with Jane and Martin Raskin, a husband and wife who practice law together in a Miami suburb.

Trump had little time. One of his top lawyers, John Dowd, had resigned over disagreements with his client, and several prominent law firms had declined to take the case. A key decision was pending about whether the president would agree to give an interview to special counsel Robert S. Mueller III.

So Trump hired the Raskins after meeting them for the first time. The decision was overshadowed by the simultaneous announcement that former New York City mayor Rudolph W. Giuliani would also join the team and take the lead in negotiating with Mueller.

But the Raskins could play as important a role if the case escalates.

They have both tried and defended clients in criminal cases and in hardball negotiations with prosecutors, skills that Trump would need if the Mueller case escalates. Among their early assignments is to try to use attorney-client protections to keep investigators from scouring Trump’s communications with his personal lawyer, Michael Cohen, who is under federal scrutiny, according to a person familiar with the president’s legal strategy who spoke on the condition of anonymity to discuss confidential discussions.

Jane Raskin has a long-ago work connection with Mueller, which associates said could be a plus to Trump’s legal team. She prosecuted Mafia underbosses for a federal Organized Crime Strike Force in Boston when Mueller held supervisory positions in the U.S. attorney’s office there. Mueller closely tracked her work, according to associates.

She also has a reputation for independence: During the Reagan administration, she resigned in protest from a criminal division post in the Justice Department over the actions of Attorney General Ed Meese.

Martin Raskin headed the criminal division in the U.S. attorney’s office in Miami. After his marriage to Jane, the couple opened a two-person firm, Raskin & Raskin, in Coral Gables, specializing in white-collar defendants.

“Both Marty and Jane, with their DOJ background, they know their way around the system,” said David S. Weinstein, a former prosecutor who is a partner at Miami-based Hinshaw & Culbertson and knows the couple well. “Contrary to the way Giuliani is portrayed as a ‘yes man,’ Marty and Jane are not going to tell their client what they think they want to hear. They will give a realistic picture of what is going on.”

Giuliani on Tuesday met with Mueller to discuss a possible presidential interview, according to three people. He did not respond to a request for comment. The Raskins declined to comment.

Trump’s difficulties in filling his legal team have included the reluctance of some firms to be associated with him and concerns about conflicts of interest with other clients, according to people familiar with the discussions. Trump is also known for ignoring legal advice, the people said. Trump had considered hiring the husband-and-wife couple of Joseph diGenova and Victoria Toensing in March but declined after determining they had conflicts.

The small size of the Raskins’ firm and their distance from typical Washington clients give them few, if any, conflicts of interest, which the Trump team regarded as a plus. In contrast to diGenova’s outspoken criticism of Mueller on television, the Raskins are low-profile attorneys who prefer to work out of the spotlight and have not commented on the investigation.

Jane Serene, as Raskin was known before her marriage, worked early in her career as a private attorney, and her clients included the Boston Globe. In the mid-1980s, after joining the federal strike force, she took on one of the prosecutions of the New England mob. She was the lead prosecutor in a successful 1987 case against underboss Ilario M.A. Zannino, who she told the court was “most assuredly one of the most vicious and ruthless criminals ever to be sentenced in this district.”

While the strike force reported directly to the Justice Department in Washington, Mueller closely monitored its work.

“Mueller admired the fact that she took on the Mafia and organized crime,” said Mark E. Robinson, who worked at the time with both of them. “He saw things very much as good guys and bad guys, and Jane went after the bad guys, and he liked that.”

Robinson said Jane Raskin’s knowledge of Mueller could prove useful in her role as Trump’s attorney because “she has some experience with Bob, who respected her greatly, and she respected him.”

After the mob case, Jane Raskin moved to Washington with the Justice Department and served as counsel to William Weld, who headed the agency’s criminal division and later became Republican governor of Massachusetts.

At the time, an independent prosecutor was investigating Meese over allegations of financial impropriety. With calls growing for Meese’s departure, Weld resigned in protest over Meese’s conduct, and Raskin joined him.

Robinson, who had followed Weld to the Justice Department and also resigned, said Jane Raskin’s departure demonstrated her ethics. “It was the right thing to do,” he said. “A point needed to be made publicly, regardless of personal cost, on principle.”

Meese eventually stepped down but no charges were brought against him, demonstrating the importance of a diligent defense.

“Jane was in the crucible,” Weld said, referring to her work in Boston and Washington, both of which he observed closely. He said Trump “couldn’t do better” than hiring her.

Raskin followed Weld into private practice, and she attended a legal conference where she met her future husband.

Although the Raskins are little known outside South Florida, Trump’s legal team and associates of the Raskins said in interviews this week that the couple are uniquely suited to their monumental task.

“Their breadth of experience as former federal prosecutors and also in private practice — that’s a unique skill set,” said Jay Sekulow, one of Trump’s lawyers in the Russia probe.

In their private practice, the Raskins’ best-known case involved defending an aircraft maintenance company charged in a case connected to the 1996 crash of a ValuJet plane, which killed 110 people. The Raskins won acquittal for the client on most charges, according to the Raskins’ account of the case.

The Raskins have not been prominent politically. But in the wake of the 2000 presidential campaign, the Raskins played a small role in the Florida recount, which led to the election of George W. Bush.

“If anybody has a chance to provide wise counsel and handle the circumstances, it would be them,” said Al Cardenas, a former chairman of the Florida Republican Party who went to Seton Hall Law School with Martin Raskin and knows the couple well. “They have handled their fair share of challenging clients.”

Alice Crites and Carol D. Leonnig contributed to this report.