"If these accusations are determined to be true, I don't think he's going to have any other option but to resign", Northam said.
Another possibility: Fairfax simply hangs on as he disputes the allegations.
Mr Fairfax said her statement had been "painful", but insisted he was innocent.
Many elected officials and presidential hopefuls have called for Fairfax to resign after two women went public with allegations of sexual assault this week.
Herring would become governor should both Northam and Fairfax step down.
"I have passed two full field background checks by the Federal Bureau of Investigation and run for office in two highly contested elections with nothing like this being raised before", he said.
Fairfax emphatically denied the new allegation, as he did the first leveled earlier by Vanessa Tyson, a California college professor who said Fairfax forced her to perform sexual acts on him at a Boston hotel in 2004.
Watson alleges that Fairfax raped her while they were students at Duke University in 2000, her attorney said in a statement. The first indentured servants from Africa landed on our shores in Old Point Comfort, what we call now Fort Monroe, and while - " Northam said on the show.More news: Dolly Parton, Ronstadt, Harris Reunite at MusiCares
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Virginia Sen. Mark Warner, a Democrat, held off from directly calling for Fairfax's resignation.
Delegate Patrick Hope said over the weekend that he would move forward with the impeachment process if Fairfax did not resign by Sunday night. "And these accusations are very, very serious", he said.
Looking ahead, Northam said he has asked his cabinet secretaries to come up with specific proposals to begin addressing issues of inequality, such as expanding access to healthcare, housing and transportation, and to begin reporting suggestions this week.
Part of the issue may be that Northam is not the only prominent Democrat in Virginia state government to be hit with allegations of misbehavior. In his statement on Saturday, he acknowledges both interactions with the women, but says both instances were consensual. The governor first apologized for the photo, then retracted that apology saying it was not him in the photo and he confused it with the other time he wore blackface for a Michael Jackson contest in 1984, promised to watch "Roots" to educate himself, and has thus far refused to resign. Steve Newman, the Senate's pro tem, serve as both a voting senator and temporary lieutenant governor.
A photo on Northam's 1984 yearbook page includes a photo of a person in blackface and another in a Ku Klux Klan robe.
Although the Democratic Party has taken nearly a zero-tolerance approach to misconduct among its members in this #MeToo era, a housecleaning in Virginia could be costly to them: If all three Democrats resigned, Republican House Speaker Kirk Cox would become governor. It will be very positive and you know we have a number of inequities in this country right now and in Virginia.
The Virginia Democrat spoke with CBS News about a racism scandal that's engulfing his nascent administration, and said he had learned much about white privilege and race since the scandal erupted.