“This is a time where Mr. Cohen had to put his family and their safety first,” Davis said.

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It is not clear to which “threats” Davis was referring, and Davis declined to provide more detail. A person familiar with Cohen’s account said the alleged threats have not been reported to law enforcement.

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Trump said of the claim that he had threatened Cohen: “I would say he’s been threatened by the truth. He’s only been threatened by the truth. And he doesn’t want to do that, probably for me or other of his clients.” The president has been publicly critical of Cohen for his cooperation with special counsel Robert S. Mueller III, and has suggested that Cohen’s father-in-law ought to be investigated.

Giuliani, the president’s current lawyer, has highlighted problems with Cohen’s credibility. Giuliani was particularly skeptical of Cohen after BuzzFeed News reported last week that Cohen told Mueller’s office Trump had directed him to lie to Congress — an account the special counsel disputed in an unprecedented public statement.

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“If you believe Cohen, I can get you a great deal on the Brooklyn Bridge,” Giuliani said.

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It was not immediately clear that lawmakers would easily allow Cohen to back out of his commitment to appear before them.

House Oversight Committee Chairman Elijah E. Cummings (D-Md.) and House Intelligence Committee Chairman Adam B. Schiff (D-Calif.) said in a joint statement that they “certainly understand the completely legitimate concerns for the safety and security of Mr. Cohen and his family members in light of the attacks last week by President Trump and again this past weekend by his attorney, Rudy Giuliani.”

But the lawmakers added that they had “repeatedly offered our assistance to work with law enforcement to enhance security measures for Mr. Cohen and his family,” and in their discussions with Cohen’s attorney, “not appearing before Congress was never an option.”

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“We will not let the President’s tactics prevent Congress from fulfilling our constitutionally mandated oversight responsibilities,” Cummings and Schiff said. “This will not stop us from getting to the truth. We expect Mr. Cohen to appear before both Committees, and we remain engaged with his counsel about his upcoming appearances.”

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Rep. Stephen F. Lynch (D-Mass.), who sits on the Oversight Committee, said several members of the panel “would be in favor of subpoenaing him sooner rather than later to try to get him prior to his incarceration.”

Cohen had announced to some fanfare earlier this month that he had accepted an invitation to testify from Cummings “in furtherance of my commitment to cooperate and provide the American people with answers.” The hearing seemed as if it could be eventful.

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Cohen pleaded guilty last year to multiple crimes, including lying to Congress about a possible Trump Tower project in Moscow and arranging hush-money payments to women who had alleged having had affairs with Trump. He was sentenced to three years in prison and is expected to report to prison on March 6, about a month after the date of his scheduled testimony.

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Cummings said, though, that Cohen could testify even after that.

“We can always bring him in. Even if he’s in prison,” he said. “We can bring him in. The marshals can — you know, they can make arrangements.”

Trump’s critics had hoped Cohen might, at the very least, offer unflattering revelations about the president. Cohen had claimed in court to have helped cover up Trump’s “dirty deeds.”

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Almost immediately, though, lawmakers raised questions about how much Cohen could say about the topic of greatest interest to the public — the information Cohen was said to provide to Mueller — because Mueller’s investigation is ongoing, and Cohen would probably be restricted in what he could say.

When Cohen announced he was testifying, Cummings said, “I want to make clear that we have no interest in inappropriately interfering with any ongoing criminal investigations, and to that end, we are in the process of consulting with special counsel Mueller’s office.”