The White House contender's contradictory explanations over two days have raised questions about details of the allegations from back in the 1990s and about his current ability to manage a crisis in the national spotlight. The controversy, relating to his time as head of the National Restaurant Association, has surfaced just as he's risen in national polls in the GOP nomination fight two months before the leadoff Iowa caucuses.
A lawyer for one woman who complained about Cain's behavior told The Washington Post on Tuesday she wants to talk publicly about it. According to that report, Joel P. Bennett, a Washington lawyer who specializes in employment cases, said he asked the National Restaurant Association to waive his client's confidentiality so she can respond to Cain's claims that the complaints were "totally baseless and totally false."
Bennett did not immediately return messages seeking comment from The Associated Press.
In Sunday night's original report by Politico, at least two women who had complained about Cain were said to have agreed to settlements that included stipulations that they not repeat their allegations in public.
Cain's evolving answers to questions in a host of media interviews this week led at least one rival campaign to suggest he's not being upfront about the accusations.
"If you are the front-runner and you plan to be the nominee ... be forthcoming so that you are vetted, and we don't get into a situation where you're our nominee and we find out things after the fact," John Brabender, a strategist for Rick Santorum's campaign, said at forum hosted by National Journal. "We're still waiting for clarification from the Cain campaign."
But others took a pass. "I've been focused on policy. I don't follow some of the things that you guys seem fascinated by," former House Speaker Newt Gingrich said during an appearance in Iowa.
.Will it all undermine Cain in Iowa and beyond? Iowa Gov. Terry Branstad was willing to hear the candidate out.
"Iowans are pretty fair-minded people and just because somebody makes an accusation -- anybody that is in a high-profile position is potential to have people make these kinds of accusations," Branstad said. "I think Iowans will, you know, carefully look at the real situation and not jump to any conclusions."
And there was one indication the controversy might not hurt Cain's support among the conservative Republicans who have been driving his bid: His fundraising surged on Monday. Mark Block, his chief of staff, said the campaign raised as much as $250,000 in a day, and Cain said it was one of his best fundraising days ever.
Over the past two days, Cain has admitted he knew of one agreement between the restaurant association and a woman who accused him of sexual harassment. He has said the woman initially asked for a large financial settlement but ultimately received two to three months' pay as part of a separation agreement. Cain also acknowledged remembering one of the woman's accusations against him, saying he stepped close to her to make a reference to her height, and told her she was the same height as his wife.
He has said he is not aware of agreements or settlements with any other women, though Politico -- which first disclosed the allegations -- reported that the trade group had given settlements to at least two female employees who accused him of inappropriate sexual behavior.
Beyond that, Cain has offered a series of sometimes-conflicting statements over what happened and didn't happen, and what he knew about financial payouts.
By Tuesday, Cain was chalking up the confusion to semantics, saying he was aware of an "agreement" but not a "settlement."
"It looked like I had changed my story," Cain told CNN Headline News. "I didn't change my story."
He acknowledged he'd made the problem worse for himself over the course of the previous day.
"If I could do it over," Cain said, "I would start with the last interview I did last night and make that the first interview of the day."
He was referring to his appearance on Fox News, where he spoke at length to Greta Van Susteren about details he had not divulged during at least three events earlier in the day -- and indeed had reversed himself.
Over the course of 24 hours, Cain first said he had no knowledge of settlements with any women who had complained about inappropriate sexual behavior. He later admitted he knew of one agreement.
He spent Tuesday much as he did Monday, going from interview to interview to defend himself.
The damage control amounted to a real-time crisis management test for a candidate who is just introducing himself to the country and who has based his campaign on his decades-long background in business management that includes stints at Godfather's Pizza, Pillsbury, Coca-Cola and the Department of the Navy.
At a time of 9.1 percent unemployment, Cain is pitching himself as a businessman who can solve problems.
He already was taking heat over the management of his campaign, insisting that his lack of staff in early voting states simply amounted to an unconventional approach, even as former employees griped about a candidate with no plan. Now, his approach to solving his own political predicament has raised questions about how he perform as president handling the nation's crisis.
"Where he has run into some trouble is, `does the story change?' Because when the story changes, people equate that with guilt," said Eric Dezenhall, who runs a top crisis communications firm. "The very act of a change in and of itself can suggest that there's a problem."
"Contrasts are big news, and one way to touch up someone claiming business competence is to dredge up something that says it's not true, that the competence is a phantom," Dezenhall said.
Cain has promised to surround himself with professional staff if elected president.
"Part of being a leader is surrounding yourself with good people and that is what I do," he said during a recent campaign appearance in Alabama, explaining that he doesn't believe a candidate needs to be an expert in every policy area to be a good president.
But, since the harassment allegations became public, Cain's staff has contributed to the conflicting accounts -- even offering flat denials that there was any factual basis to the story.
Separately, chief of staff Mark Block has a lawyer investigating whether a charity he founded, Prosperity USA, improperly gave goods and services to Cain's presidential campaign earlier this year.
On the harassment allegations, Cain initially told The Associated Press that he couldn't remember any details of any accusations. Hours later, he acknowledged remembering the one woman's complaint.
By Tuesday, he attributed the lapses in memory to being under so much pressure during a day of media appearances.
"After 12 hours over the day, many events, many interviews, I was able to gradually recall more and more details about what happened 12 years ago," he said. "I wasn't given the opportunity to think about it for a day before I was forced to start answering questions."
Politico said it had started asking Cain's campaign about the allegations on Oct. 20, eleven days before the story was published late Sunday.
Cain said Monday that Politico had also provided his campaign with the name of a second woman who, Politico reported, also received a settlement after complaining of sexually inappropriate encounters with Cain.
Associated Press writers Ken Thomas in Washington, Shannon McCaffrey in Georgia, and Thomas Beaumont and Philip Elliott in Iowa contributed to this report.