Embattled Rep. Michael G. Grimm’s expected guilty plea in connection with felony charges left his congressional career in question ahead of a federal court hearing set for Tuesday.

Grimm (R-N.Y.) originally pleaded not guilty to a 20-count fraud indictment handed down in April, when he was charged with tax evasion over alleged financial misconduct at a Manhattan restaurant called Healthalicious that he co-owned from 2007 to 2010.

A lawyer representing Grimm, Stuart N. Kaplan, declined any comment until after Tuesday’s hearing.

Grimm, a businessman and former FBI agent, was first elected to represent New York’s 11th Congressional District in 2010.

His congressional tenure has been marked by questions about his personal conduct. In 2011, the New Yorker reported that Grimm brandished a gun at a nightclub in 1999. Grimm called the article a “hatchet job” and denied the allegation.

In January, Grimm drew headlines when he threatened to throw a New York television reporter off a Capitol balcony. He subsequently apologized.

The indictment this spring initially seemed to threaten Grimm’s 2014 reelection prospects in his Brooklyn and Staten Island district, but he ultimately coasted to another term.

If Republican House leadership were to ask Grimm to resign when Congress returns in January, and he stepped down, a special election would be held to fill the seat.

Should Grimm decline to ­resign, House GOP leaders believe the House’s code of conduct could force him to abstain from congressional activities, according to a House Republican aide who requested anonymity to speak freely about internal discussions.

The aide pointed to a clause in Rule 23 as a guide for the leadership as it considers its response. The clause states that a member who has been convicted of a crime “for which a sentence of two or more years’ imprisonment may be imposed should refrain from participation” in committees and from “voting on any question at a meeting of the House,” until the member is “reelected to the House after the date of such conviction.”

Aides to House Speaker John A. Boehner (R-Ohio) and House Majority Leader Kevin McCarthy (R-Calif.) declined comment Monday on the news of Grimm’s plea. But when asked about Grimm’s legal troubles in April, Boehner said, “I think all members should be held to the highest ethical standards.” He also supported Grimm’s decision at the time to temporarily step down from the House Financial Services Committee.

Rep. Peter T. King (R-N.Y.) said Monday that he had been informally counseling Grimm in recent weeks. He declined to comment on Grimm’s plea.

“Michael Grimm has been an effective congressman and I wish him well as he gets on with his life,” King said.

Michael R. Long, the chairman of the Conservative Party in New York, urged Grimm to fight to stay in office.

“He should not resign unless it is necessary,” Long said Monday. “He’s doing a very good job and he’s certainly not the first congressman who was involved in tax evasion.”

Jose A. DelReal contributed to this report.