New York State Governor Eliot Spitzer has been given a deadline to step down or face impeachment proceedings over allegations that he hired a prostitute.
His top Republican opponent in the New York Assembly gave him up to 48 hours - until early on Thursday - to resign.
Mr Spitzer has not admitted paying for sex, but he did tell a news conference that he had let down his family.
There is also speculation he might face criminal charges, amid a reported inquiry into financial transactions.
The allegations against Mr Spitzer, a high-profile Democrat who campaigned for ethical leadership, have caused widespread shock in New York and US political circles.
The Wall Street Journal quoted "a person close to" the governor as saying he was likely to resign, perhaps by the end of the day.
New York Assembly Republican Minority Leader James Tedisco said: "If he does not resign within the next 24 to 48 hours, we will prepare articles of impeachment to remove him.
"We need a leader in place that has the support of people on both sides of the aisle," Mr Tedisco told reporters.
The assemblyman's spokesman told the BBC that the business of state government would be paralysed until Mr Spitzer left office.
The Republicans would need support from the Democratic majority in the assembly to start impeachment proceedings.
The BBC's Adam Brookes in Washington says Mr Spitzer has taken on a big Manhattan law firm - possibly in anticipation of being charged.
The investigation began last year when banks reported irregular transfers to the Internal Revenue Service, which traced them back to Mr Spitzer and discovered they were made to a high-priced prostitution ring, an unnamed law enforcement official told the Associated Press (AP) news agency.
SPITZER SCANDAL TIMELINE
2007 Internal Revenue Service reportedly begins investigating Eliot Spitzer, after banks report suspicious transfers
12-13 Feb, 2008 Spitzer allegedly heard on federal wiretap arranging to meet woman at Washington hotel
13 Feb Spitzer allegedly rents room for "Kristen" at Mayflower Hotel and sneaks past his police guard to meet her
6 Mar Four other people charged with operating prostitution ring
11 Mar NY Times breaks story, saying Spitzer has called aides to emergency meeting; Spitzer tells press conference he has let down his family
Allegations based on law enforcement sources quoted by Associated Press and New York Times
The account of events matched that reported earlier by the New York Times.
Mr Spitzer, 48, was overheard during a surveillance operation arranging to meet a woman - "Kristen"- in a Washington hotel last month, the AP source alleged.
Kristen was described by the prostitution agency as a "petite, pretty brunette", according to a federal court document, the source said.
Investigators had found that Mr Spitzer was a repeat customer with the agency, called the Emperors Club VIP, the official said.
He allegedly paid more than $4,000 for the woman's services.
No charges have been brought against Mr Spitzer, and he has not admitted any offence.
But he did tell a packed press conference at his Manhattan office: "I have disappointed and failed to live up to the standard I expected of myself.
"I must now dedicate some time to regain the trust of my family," he added, as his wife of two decades, Silda, stood by his side.
There was little sympathy on display for Mr Spitzer, a first-term Democratic governor who was known for his relentless pursuit of office-holders suspected of wrongdoing.
HAVE YOUR SAY
Political machinery in New York's capital will force Eliot Spitzer's resignation
Andy, New York, USA
An editorial in the Wall Street Journal said: "Governor Spitzer, who made his career by specialising in not just the prosecution, but the ruin, of other men, is himself almost certainly ruined."
Kenneth Lovett, of the New York Post, said: "It's hard to see how he can remain as governor - or why he should."
Mr Spitzer, a father-of-three, was elected governor in November 2006.
As New York's attorney general, he had become known as "the sheriff of Wall Street" for his campaign against financial crime.
His successes in that battle led Time Magazine to name him "Crusader of the Year" in 2002.
Mr Spitzer has been a close ally of New York Senator Hillary Clinton, and a prominent supporter of her campaign to be the Democratic nominee for president.
This scandal is embarrassing for her, and he will make things difficult for her if he does not resign quickly, says the BBC's North America editor, Justin Webb.