Some of the governor’s allies have argued that if Mr. Northam can weather the short-term frenzy, the bully pulpit of public office may offer him his surest path to redemption, and to making amends with constituents who feel betrayed.

Indeed, some of the Democrats who demanded his resignation have already begun curbing the efforts to force him out, and the governor has been meeting with some of his critics.

“I don’t think that he would have invited us if he was not remorseful,” said Dr. Charles Steele Jr., the president of the Southern Christian Leadership Conference, who had previously called for Mr. Northam’s resignation but met with the governor on Wednesday at the Executive Mansion.

Dr. Steele, whose organization’s first president was the Rev. Dr. Martin Luther King Jr., said he and the governor discussed reconciliation, and not the politics of a resignation. But Mr. Northam has not had to look far into history for precedents of governors hunkering down in office despite scandals.

Robert Bentley of Alabama managed to last more than a year after he was accused of sexual misconduct. In Illinois, Rod Blagojevich, who was accused of trying to trade away a Senate seat, clung to office until he was impeached and removed by the Legislature. Eric Greitens of Missouri resigned, but only after a rocky four-and-a-half months that included a felony indictment. One of Mr. Northam’s predecessors in Virginia, Robert F. McDonnell, endured some calls for his resignation and finished his term under a legal cloud. (He was later found guilty of conspiracy, bribery and extortion, but the United States Supreme Court overturned his convictions.)

And Mark Sanford of South Carolina acknowledged an extramarital affair in 2009 but stayed through the end of his term in 2011, and was later elected to Congress.

“If you really go back and look at it in an even-keeled way, Sanford benefited from staying in office,” said Mr. Bauer, who stood to succeed Mr. Sanford. “Had Sanford just resigned, it would have been great for André, but he would have left on a low point. He stayed in office and reinvented himself with the time he had left. History will judge him on his whole period, and not just leaving office.”