Michael Cohen’s testimony on Monday in the criminal prosecution of President Trump could prove to be a make-or-break moment for Manhattan district attorney Alvin Bragg. Cohen’s long history as Mr. Trump’s personal lawyer and fixer puts him at the center of the alleged payment to adult film actress Stormy Daniels, but his past conviction for lying to Congress may be enough for defense attorneys to convince the jury that Cohen is not credible. 

Cohen, who worked for Mr. Trump from 2007 to 2018, will appear in the Manhattan courtroom as a star witness for the prosecution on Monday morning. He will be asked about his involvement in the alleged hush money scheme and how Mr. Trump allegedly broke the law by billing the supposed campaign contribution as a legal expense. 

Prosecutors have alleged — and Cohen has admitted — that the longtime Trump fixer paid $130,000 to the adult film star in the weeks leading up to the 2016 election in order to keep the affair out of the headlines. Cohen has stated that he set up a Delaware shell company, Essential Consultants LLC, in order to facilitate that payment, for which Mr. Trump later reimbursed him. 

During a 2019 hearing before the House Oversight Committee, Mr. Cohen detailed this “catch and kill” scheme that involved buying life rights in order to stop any details about Mr. Trump’s alleged affairs from being published. 

“Catch and kill is a method that exists when you’re working with a news outlet — in this specific case it was AMI, National Enquirer, David Pecker, Dylan Howard, and others — where they would contact me or Mr. Trump or someone and state that there’s a story that is percolating out there that you may be interested in,” he said. “So then you contact that individual and purchase the rights to that story from them.”

Cohen said at the time that he was “involved in several of these catch and kill episodes” with Mr. Trump. 

Cohen’s credibility has been questioned voraciously over the years by Republicans — a tactic that will likely be employed by the former president’s lawyers during cross-examination. Just on Wednesday, the chairmen of the House Judiciary and Oversight Committees, Congressmen Jim Jordan and James Comer, sent a letter to the Justice Department asking that Cohen be investigated for lying to Congress in 2019. 

“Committees learned that Cohen separately lied … before the House Permanent Select Committee on Intelligence in a 2019 deposition. Cohen’s testimony is now the basis for a politically motivated prosecution of a former president and current declared candidate for that office,” the chairmen write. 

During the 2019 Oversight Committee hearing, Cohen detailed the work he did for Mr. Trump for more than a decade. Republicans attacked him right out of the gate as an uncredible witness, given he had already been convicted of lying to the legislative branch.

“Your first announced witness, Michael Cohen … is a guy who is going to prison in two months for lying to Congress,” Mr. Jordan, who at the time was the ranking member of the committee, said in his opening statement. “This might be the first time someone who has been convicted of lying to Congress has so quickly returned to Congress.”

The jurist overseeing the case, Judge Juan Merchan, has already told Cohen to temper his criticism of the former president even before he has taken the stand. At the end of a hearing on Friday, Judge Merchan told prosecutors that they had to stop him from commenting on the case publicly after he was seen on the social media app TikTok wearing a shirt with a picture of Mr. Trump behind bars. 

“I would direct the people to communicate to Mr. Cohen that the judge is asking him to refrain from making any more statements about this case,” Judge Merchan said. “That comes from the bench and you are communicating that on behalf of the bench.”