ORLANDO, Fla. — A former local official in Florida facing an array of federal charges in an inquiry that is also focused on Representative Matt Gaetz was expected to plead guilty, lawyers said in court on Thursday, an indication that the defendant is likely to cooperate as a key witness against Mr. Gaetz.

A cooperation agreement by Joel Greenberg, a former county tax collector north of Orlando, is almost certain to create legal difficulties for Mr. Gaetz, a prominent ally of former President Donald J. Trump. Investigators are said to be examining their involvement with women who were recruited online for sex and given cash payments, as well as whether Mr. Gaetz had sex with a 17-year-old. Mr. Greenberg, who already faces one count of sex trafficking involving the girl, would be able to give prosecutors a firsthand account of their actions.

Mr. Greenberg faces other charges, including stalking a political rival and trying to bribe a federal official; he has pleaded not guilty. Investigators suspect he met the women through a website that connects people willing to go on dates in exchange for gifts and allowances, then arranged for liaisons with himself and associates including Mr. Gaetz.

Mr. Greenberg’s potential deal also comes as the F.B.I. has widened its investigation to include questions about a trip to the Bahamas that Mr. Gaetz took with Republican allies from Florida and women who were asked to provide sex for them, according to four people familiar with the inquiry.

Investigators have also been told of a conversation where Mr. Gaetz and a prominent Florida lobbyist discussed arranging a sham candidate in a State Senate race last year to siphon votes from an ally’s opponent, according to two people familiar with the investigation. They cautioned that that aspect of the inquiry, which could broaden it beyond sex trafficking, was in its early stages.

Mr. Gaetz’s legislative director in Washington, Devin Murphy, abruptly quit last week, three people familiar with the decision said on Thursday, becoming the second senior aide to resign since the Justice Department inquiry came to light. And late Thursday, Adam Kinzinger of Illinois became the first Republican representative to call on Mr. Gaetz to step down.

“I’m sure Matt Gaetz is not feeling very comfortable today,” Mr. Greenberg’s lawyer, Fritz Scheller, told reporters outside the federal courthouse in Orlando. He and a Justice Department prosecutor, Roger Handberg, both disclosed Mr. Greenberg’s expected plea during an earlier six-minute hearing.

Mr. Gaetz, 38, has denied that he paid for sex or had sex with a minor. A lawyer for Mr. Gaetz said that many of the allegations being made about Mr. Gaetz were false. “In your apparent rush to grab a headline, your story contains numerous false facts which call into question your sources — both as to their credibility and to the source of their knowledge,” said the lawyer, Geoffrey R. Johnson.

Mr. Gaetz’s office declined to comment about Mr. Murphy’s departure but did not respond to requests for comment about Mr. Greenberg’s potential plea deal or the sham candidate discussion.

However, Mr. Gaetz’s office also separately released a statement that said women on his staff have always found him to be “a principled and morally grounded leader.”

“At no time has any one of us experienced or witnessed anything less than the utmost professionalism and respect. No hint of impropriety. No ounce of untruthfulness,” said the statement, which no one signed by name.

A Justice Department spokesman declined to comment.

Mr. Greenberg had been scheduled to go on trial in June, but on Thursday both sides set a May 15 deadline for a plea deal. If they do not reach one, the case would go to trial in July, they agreed.

Neither Mr. Scheller nor Mr. Handberg said explicitly that Mr. Greenberg, 36, had agreed to cooperate with the continuing investigation. He faces a mandatory minimum of 12 years in prison and decades more should he be found guilty on all charges and given maximum sentences.

If Mr. Greenberg hopes to reduce his sentence, legal experts said, he would have to fully cooperate with Justice Department prosecutors, including being candid with investigators and testifying at trials and before grand juries in related investigations.

Bahamas Trip

Among the matters under scrutiny in the investigation is a trip that Mr. Gaetz took to the Bahamas with Republican allies including Jason Pirozzolo, an Orlando-based surgeon who has raised funds for Gov. Ron DeSantis of Florida, and a group of women, according to four people with knowledge of the inquiry. The trip occurred sometime after Mr. Gaetz was elected to Congress.

The F.B.I. has questioned witnesses about whether the women had sex with the men on the trip in exchange for money and free travel and about whether they used drugs; it is illegal to engage in sex in exchange for something of value if the government can prove that it involved force, fraud or coercion.

Federal investigators in December questioned one woman who was part of the trip and seized her phone, according to two of the people.

Immigration authorities stopped one of two planes taken by the group on its return to the United States, in Fort Lauderdale, Fla., three of the people said. It is unclear why the plane was stopped, but two of the people said that among those aboard was Halsey Beshears, who served in Mr. DeSantis’s administration until he resigned in January, citing health reasons.

Mr. Beshears did not respond to requests for comment. David Bigney, a lawyer for Mr. Pirozzolo, declined to comment. CBS News first reported that investigators were scrutinizing the trip.

Both are prominent in Florida Republican circles. Mr. Beshears served as a state representative from the Florida Panhandle before Mr. DeSantis announced in 2018 that he had appointed him to lead Florida’s Department of Business and Professional Regulation.

Mr. Pirozzolo supported Mr. DeSantis’s campaign for governor, hosting an event at his house in 2018 where Mr. Greenberg and Mr. Gaetz both spoke, according to social media posts and video of the event. Mr. Gaetz praised Mr. DeSantis for his tough stand against sexual harassment.