Republican congressman Michael Grimm pleaded guilty to one count of felony tax evasion on Tuesday at a federal court in Brooklyn, weeks after he was overwhelmingly re-elected to a third term in Congress.

Grimm had been hit with a 20-count indictment in April over practices at his New York restaurant, Healthalicious. The charges included perjury, employing undocumented immigrants and concealing more than $1m in wages and sales.

“I made some very big mistakes … But I also accept full responsibility,” he told reporters outside court after he entered his plea. “As long as I’m able to serve, I’m going to serve.”

The judge in the case has scheduled Grimm’s sentencing for 8 June. Prosecutors are seeking a sentence of between 24 and 30 months, while the defense is asking for 12 to 18 months.

As reports that Grimm would plead guilty started to trickle out beginning on Monday, Democratic leaders in the House of Representatives began to call for the House speaker, John Boehner, to force Grimm to step down. “Now that the election is over, Congressman Grimm is finally admitting the truth to his constituents. Clearly, Speaker Boehner must insist that Congressman Grimm resign immediately,” the House minority leader, Nancy Pelosi, said in a statement.

“Speaker Boehner has let this go on long enough. It’s past time for Michael Grimm to go and it’s Boehner’s responsibility to make it happen,” the Democratic Congressional Campaign Committee wrote on Twitter on Tuesday. During Grimm’s 2014 re-election campaign, the DCCC had gone all out to unseat him, spending millions and even creating a “Casefile” micro-site chronicling his alleged misdeeds. Its efforts were in vain; Grimm trounced his Democratic challenger, Domenic Recchia, despite the indictments hanging over his head.

Boehner’s spokesman told Politico that there would be no announcement from his office until the speaker had discussed the matter with Grimm. But if Grimm does not want to resign from Congress, he doesn’t actually have to. According to the Congressional Research Service, “Members of Congress do not automatically forfeit their offices upon conviction of a crime that constitutes a felony.” The members of the House could, if they chose to do so, vote to expel Grimm, but it would probably be a messy and protracted process, and it happens very rarely – the last member to be expelled to be expelled was James Traficant, an Ohio Democrat who was kicked out of Congress in 2002.

According to an indictment, the tax fraud began in 2007 after Grimm retired from the FBI and began investing in a small Manhattan restaurant called Healthalicious. The indictment accused him of underreporting more than $1m in wages and receipts to evade payroll, income and sales taxes, partly by paying immigrant workers, some of them in the country illegally, in cash.

When he was initially charged, Grimm called the case “a political witch-hunt” and declared, “I’m a moral man, a man of integrity.”