The public hearing is one of three sessions Mr. Cohen will have next week on Capitol Hill. He is also scheduled to participate in private deposition-style interviews with the House and Senate Intelligence Committees, where he is likely to be pressed on matters pertaining to Russia and other potential efforts by foreign powers to gain influence over Mr. Trump. Mr. Cohen pleaded guilty in November to lying to the two intelligence committees about the Trump Organization proposal to build a skyscraper in Moscow.

Before that, in August, Mr. Cohen had pleaded guilty in federal court in Manhattan to tax fraud, making false statements to a bank and the campaign finance violation. He said in court at the time that the last violation was the result of payments he made at Mr. Trump’s behest during the 2016 campaign to two women to keep them from speaking publicly about affairs they said they had with Mr. Trump.

Mr. Cohen had been expected to report early next month to begin serving a three-year prison sentence, but on Wednesday, a federal judge in Manhattan said that he could delay that appearance by two months, to May 6. In requesting the delay, Mr. Cohen’s lawyers said he had undergone recent shoulder surgery and needed to take part in physical therapy.

If Democrats are hoping that Mr. Cohen’s testimony will damage Mr. Trump’s public image, Republicans have been laying the groundwork to try to undercut Mr. Cohen’s credibility first. In a letter to Mr. Cummings on Tuesday, the oversight committee’s top Republicans referred to Mr. Cohen as “an admitted serial liar” and accused the Democrats of putting on a political show.

“When Cohen appears before our committee, we can only assume that he will continue his pattern of deceit and perjury,” the Republicans, Representatives Jim Jordan of Ohio and Mark Meadows of North Carolina, wrote. “Although Cohen falsely attributes his crimes to ‘blind loyalty to Donald Trump,’ a federal judge correctly noted that Cohen’s crimes were all motivated by his personal greed and ambition.”

Mr. Trump himself has repeatedly suggested that Mr. Cohen lied to prosecutors about him to reduce his own prison sentence. Rudolph W. Giuliani, Mr. Trump’s lawyer, abruptly shifted his own assessment of Mr. Cohen’s honesty after Mr. Cohen pleaded guilty and began talking to prosecutors.