A plea by the former elected official, Joel Greenberg, could significantly strengthen the Justice Department’s hand as it investigates Mr. Gaetz and others who met Mr. Greenberg through Florida Republican politics and are being scrutinized on potential sex trafficking violations. Mr. Greenberg met women through a website that connects people who are willing to go on dates in exchange for gifts and allowances, then introduced them to Mr. Gaetz, who along with Mr. Greenberg had sex with them, people familiar with the matter have said. The prosecutor, Roger Handberg, made the disclosure about Mr. Greenberg’s case at a six-minute status hearing at the federal courthouse in Orlando, as did Mr. Greenberg’s lawyer, Fritz Scheller. Mr. Greenberg had been scheduled to go on trial in June, but both sides set a May 15 deadline for a plea deal. If they do not reach an agreement, the case would go to trial, they agreed. “We believe this case is going to be a plea,” Mr. Handberg said.