This post has been updated
For now at least, Grimm does not plan to do that. Stuart N. Kaplan, an attorney for Grimm, said in an e-mail that the congressman does not plan to resign.
Grimm could face up to three years in prison. He is scheduled to be sentenced June 8.
The congressman was indicted this year on 20 counts of misconduct in connection with a Manhattan health food restaurant he co-owned before he became a member of Congress. As a part of his plea, the other charges will be dismissed without prejudice, Kaplan said.
In anticipation of Grimm's plea, top Democrats ramped up calls for him to resign hours before he appeared in court.
In statements released Tuesday morning, House Minority Leader Nancy Pelosi (D-Calif.) and the Democratic Congressional Campaign Committee called on House Speaker John A. Boehner (R-Ohio) to press Grimm to step aside.
“Now that the election is over, Congressman Grimm is finally admitting the truth to his constituents," Pelosi said in a statement.
Before Grimm submitted his plea, Boehner spokesman Michael Steel did not indicate whether the speaker would ask Grimm to resign.
"We won't have any announcements until the Speaker discusses the matter with Mr. Grimm," said Steel in an e-mail.
In a 30-page indictment released in late April, Grimm was accused by prosecutors of wage and payroll fraud, tax evasion and hiring illegal immigrants at Healthalicious, an Upper East Side Restaurant Grimm co-owned from 2007-2010. Prosecutors said he also lied under oath.
The Republican caught a break when a judge ruled that his trial would not begin until after the Nov. 4 election. Instead, it was slated to begin Feb. 2.
Grimm defeated Democratic challenger Domenic Recchia, even as Democrats ran TV advertisements that sought to remind voters about the incumbent's legal woes.
First elected in 2010, Grimm represents a district that includes Staten Island and parts of Brooklyn. He is a former FBI agent with a reputation for being intense and at times combative.
After President Obama's State of the Union address this year, Grimm threatened to throw a reporter off a balcony after the reporter questioned him about his legal standing. He later apologized.
If Grimm changes his mind and decides to resign, it will be up to New York Gov. Andrew Cuomo (D) to decide whether to hold a special election to fill his seat, which could be at risk of falling into Democratic hands. Obama won 52 percent of the district in 2012.
Local party activists would decide who to nominate in a special election.
If the congressman declines 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.
"If things don't go my way, and I had to step down in January, then there will be a special election," Grimm told WABC radio in October. "At least the people of Staten Island and Brooklyn would have qualified people to choose from."
Paul Kane and Robert Costa contributed to this post