Herman Cain’s campaign is under fire on several fronts this week, and the swift and unpredictable rise of his political fortunes might suffer a death of a thousand cuts as criticisms mount ever higher. As Chris Cillizza reported:

When Politico first reported late Sunday night that businessman Herman Cain had faced accusations of sexual harassment in the 1990s, the frontrunning presidential candidate had a choice: admit his error or fight like hell against the story.

He, not surprisingly, chose the latter option — casting the report as a “witch hunt” organized by the very establishment he has rocked to its core with his rapid rise in polling over the last six weeks.

The political problem with the path Cain chose is that it requires him to have an airtight — and unchanging — explanation for his conduct that can prove, beyond a reasonable doubt, that he is the victim of an unfair attack. And that’s not what happened over the past 24 hours.

Cain first denied any knowledge of settlements paid out to women who brought the allegations again him during his time as head of the National Restaurant Association.

But, in an interview with Fox News Channel’s Greta van Susteren that aired Monday night, Cain acknowledged that he was aware of a payout to one of the women.

“My general counsel said this started out where she and her lawyer were demanding a huge financial settlement,” Cain told van Susteren. “I don’t remember a number. … But then he said, because there was no basis for this, we ended up settling for what would have been a termination settlement.”

Cain allies — the likes of conservative radio talk show hosts Rush Limbaugh and Laura Ingraham came to his defense on Monday — will likely dismiss the inconsistencies as nothing more than a misremembered episode from more than a decade ago.

But changing your story in even a small way leads to lots and lots more questions about what else Cain either got wrong or misremembered.

Herman Cain and his campaign were on the defensive Monday after the allegations of sexual harassment surfaced. Cain denied the allegations, as Philip Rucker, Sandhya Somashekhar and Nia-Malika Henderson reported:

Herman Cain emphatically denied on Monday that he had ever sexually harassed anyone, calling allegations of harassment by two former employees “totally baseless and totally false” and saying that he is the innocent victim of a “witch-hunt.”

With the allegations threatening his bid for the Republican presidential nomination, Cain acknowledged in an interview with Fox News Channel the harassment charges during his tenure as head of the National Restaurant Association. He said he had been “falsely accused.”

Later Monday, during an appearance at the National Press Club, Cain said that “in all of my over 40 years of business experience — running businesses and corporations — I have never sexually harassed anyone.”

“I was falsely accused of sexual harassment and when the charges were brought, as the leader of the organization, I recused myself and allowed my general counsel and my human resource officer to deal with the situation, and it was concluded after a thorough investigation that it had no basis,” Cain said.

Politico reported Sunday night that Cain had sexually harassed two women while he ran the trade association during the 1990s and that the women were given financial settlements and left the association.

Cain said that he was “unaware of any sort of settlement. I hope it wasn’t for much, because I didn’t do anything.’

Cain suggested that the report was the product of a “witch hunt” spurred by his recent surge in the polls in the GOP presidential contest.

“This bull’s-eye on my back has gotten bigger. We have no idea the source of this witch-hunt, which is really what it is,” Cain said during a question-and-answer session following a 25-minute campaign speech before the National Press Club in downtown Washington. Cain’s comments were broadcast live on national cable-television news networks.

Many analysts are asking what effect this could have on Cain’s campaign given its meteoric rise in the polls over the past several weeks. As Chris Cillizza explained:

While the first reaction from the Cain campaign isn’t a bad strategic move — try to turn the story into the latest episode of the mainstream media having it out for a conservative — the detailed nature of the Politico article will make it tough for him to simply stand by that first statement.

At some point — and that point is likely very soon — Cain is going to have to issue a public accounting that makes clear to reasonable people that these allegations were spurious and without merit. In the absence of such proof, rhetoric alone is very unlikely to save him from a flurry of questions asking for more information about the allegation. And the fewer answers he has, the more questions will get asked.

We may know more as soon as today because — in a fit of tremendous timing for political reporters and less-tremendous timing for Cain — he will be in Washington, D.C., for the better part of the day; he is scheduled to appear in the morning at the American Enterprise Institute to discuss his “9-9-9” tax reform plan and then at a National Press Club at a luncheon.

Predicting how stories like this one will play out are virtually impossible. (We still remember well when we genuinely thought South Carolina Gov. Mark Sanford was hiking the Appalachian Trail.)

It’s possible that Cain is able to beat the story back with a detailed accounting of just what happened. It’s also possible that the story heads in all sorts of directions that Cain’s still-spartan staff aren’t able to control.

“Bill Clinton’s campaign survived this and much worse,” said Ari Fleischer, a Republican strategist and former White House press secretary. “Plus, the normal rules don’t seem to apply to an outsider like Cain.”

At a minimum, the story will serve as a week-long (and probably longer) distraction for Cain, who was hoping to use the next few weeks to prove to the political class he could raise the money and put together the sort of organization that could make him a real rival to former Massachusetts governor Mitt Romney.

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