Cohen, who said in court last year that he once worked to cover up Trump’s “dirty deeds,” will return to the Hill on Wednesday, where those familiar with his testimony say he is expected to describe personal, behind-the-scenes encounters that portray Trump as a lying racist and provide what Cohen’s supporters say they believe is evidence that Trump broke the law after he was sworn in.

But Cohen — who was convicted of lying to Congress and whose allies have been known to exaggerate or misstate the information he possesses — will have to withstand attacks on his credibility. The strength and reliability of his anticipated claims about the president’s possible wrongdoing could not immediately be ascertained.

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On Tuesday, as those familiar with his testimony briefed reporters on what he would probably say, the White House dismissed Cohen as a “disgraced felon” who was “going to prison for lying to Congress,” while a Republican congressman leveled a lurid allegation — without evidence — about Cohen’s personal life.

“Do your wife & father-in-law know about your girlfriends?” Rep. Matt Gaetz (R-Fla.) wrote in a tweet. “Maybe tonight would be a good time for that chat. I wonder if she’ll remain faithful when you’re in prison. She’s about to learn a lot.”

Lanny J. Davis, an attorney for Cohen, said of Gaetz’s comment: “We will not respond to Mr. Gaetz’s despicable lies and personal smears, except to say we trust that his colleagues in the House, both Republicans and Democrats, will repudiate his words and his conduct. I also trust that his constituents will not appreciate that their congressman has set a new low — which in today’s political culture is hard to imagine as possible.”

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A long-serving Democrat, Rep. Bill Pascrell Jr. (N.J.), called for an internal inquiry, calling Gaetz’s accusation “grossly unethical and probably illegal” in a tweet mentioning a section of the U.S. Code that addresses witness tampering. “House Ethics must investigate this disgrace and stain on our institution,” Pascrell wrote.

Cohen seemed undeterred with proceeding as planned.

“At this point in time, I really appreciate the opportunity that was given to me to clear the record and to tell the truth,” he said as he emerged Tuesday from private testimony before the Senate Intelligence Committee. “And I look forward to tomorrow, to being able to in my voice, to tell the American people my story, and I’m going to let the American people decide exactly who’s telling the truth.”

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Cohen, who previously canceled an appearance on Capitol Hill citing alleged threats from Trump and his allies, testified for nine hours Tuesday, though details of what he said were scant. Lawmakers remained tight-lipped as they entered and exited the secure chamber in which the interview took place, walking swiftly past television cameras and mostly ignoring reporters’ questions about Cohen’s testimony and demeanor.

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Those who did make statements offered little in the way of specifics.

“Two years ago, when this investigation started, I said it may be the most important thing I’m involved in my public life in the Senate,” said Sen. Mark R. Warner (Va.), the Senate Intelligence Committee’s top Democrat. “And nothing I heard today dissuades me from that view.”

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The testimony before the committee had been expected to focus on Russia and what — if any — evidence Cohen could provide about possible coordination between the Trump campaign and the Kremlin to influence the 2016 election. Cohen is scheduled to appear again Thursday before the House Intelligence Committee to discuss similar topics, also behind closed doors.

The marquee event, though, is likely to come Wednesday, when Cohen testifies in public before the House Oversight Committee. That hearing will be wide-ranging, examining Trump’s personal finances, his compliance with campaign finance and tax laws, and myriad other topics.

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Cohen is expected to describe to lawmakers what he views as Trump’s “lies, racism and cheating,” both as president and in private business, and will describe “personal, behind-the-scenes” interactions he witnessed, a person familiar with the matter said. Perhaps more explosively, he is expected to provide accounts of possible criminal conduct that occurred while Trump was in office, according to two people familiar with his testimony.

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It was not immediately clear what those accounts or alleged conduct might be, though one of the people familiar said it had to do with the hush-money payments Cohen helped arrange to buy the silence of women who alleged having affairs with Trump years ago, before he became president. That person said Cohen will provide lawmakers an exhibit to support his assertion; another person said he would provide “very specific details” about the payments, some of which have not been made public.

The people spoke on the condition of anonymity because they were not authorized to discuss Cohen’s expected testimony on the record, and they refused to provide any more details. It was not immediately clear whether Cohen already had provided his purported evidence to federal prosecutors in the U.S. District Court for Southern District of New York, with whom he has said he will continue to cooperate.

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Cohen pleaded guilty last year in New York to violating campaign finance laws — saying he did so at Trump’s direction — and committing other financial crimes. Trump’s representatives have disputed claims that Trump was involved in violating campaign finance laws and that he had the alleged affairs.

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Cohen separately pleaded guilty to lying to Congress about a possible Trump Tower project in Moscow. He was sentenced to three years in prison for all of his crimes, and is expected to begin serving that term in May.

Rudolph W. Giuliani, Trump’s lawyer, said Tuesday, “I don’t know what he’ll say, but we are confident that whatever he says could point to criminal activity by him, not the president.”

He said Trump’s legal team was “not bothering” the president, who was focused on his work in Vietnam.

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The relationship between Trump and Cohen has been fractured since Cohen pleaded guilty and began cooperating with law enforcement, including special counsel Robert S. Mueller III. Trump has termed Cohen a “rat,” suggested his father-in-law should be investigated and contrasted Cohen unfavorably with his former campaign chairman, Paul Manafort, who was accused of lying to Mueller’s team even after he agreed to cooperate.

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But Cohen’s testimony Wednesday is sure to inflame those tensions — even as the president is abroad in Vietnam.

Cohen’s allies hope he could become this generation’s John Dean — President Richard M. Nixon’s White House counsel who famously testified to the Senate about Nixon’s involvement in the Watergate scandal that ultimately led him to resign. He is expected to detail his motives for having helped Trump and for now ostensibly coming clean, the person familiar with the matter said, in hopes of allaying concerns about his past misstatements.

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Cohen also is expected to “provide more detail about his lies to Congress” and address in some capacity a BuzzFeed News report asserting he told Mueller’s office that the president directed him to lie, the person said. The special counsel has disputed that report, though Cohen has not said anything about it publicly.

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Cohen also is expected to present records of Trump’s finances and recall alleged instances “where Trump used high numbers for his purposes, such as getting on the top 10 wealthiest people on the Forbes list, and low numbers, when it came time to paying real estate taxes,” the person said.

The Wednesday hearing is scheduled to begin at 10 a.m.