Herman Cain makes a point during a speech at a campaign rally, Wednesday, Nov. 30, 2011, in Dayton, Ohio. Cain claimed a "groundswell of positive support" from backers for his presidential campaign. (Al Behrman/AP)

Faced with a critical question, Newt Gingrich often responds by criticizing the questioner. Mitt Romney reacts with a kind of gee-willikers frustration.

But Herman Cain, whose problems have transfixed the Republican presidential campaign, has used a different strategy. The businessman often responds to trouble with a flat, short answer: Whatever it is, it isn’t true.

His denials usually come with little or no explanation. When other candidates — not to mention economists — began to find flaws in his “9-9-9” tax plan, Cain responded, “All those are simply not true.”

When allegations of sexual harassment were first raised against him, Cain denied any validity to them. “Totally baseless and totally false,” he said, denying that there was any settlement in the cases.

But the trouble with this tactic is that it doesn’t work if the first answer doesn’t hold up.

Voters have now twice seen Cain return to explain that the story was more complicated than he first let on. The 9-9-9 plan did need a tweak, after all. And there had been a sexual harassment settlement, despite what he said.

Now, Cain’s campaign seems to be riding on his latest blanket denial: that there is no truth to the accusation that he had a 13-year affair with a Georgia woman. A “fabricated, unsubstantiated story,” he said in an e-mail sent to supporters on Tuesday.

“They want you to believe if they do enough character assassination on me, I’m going to drop out,” Cain told a crowd of dozens in Dayton, Ohio, on Wednesday. “I happen to believe that the American people have a different idea.”

A day after Cain said he was “reassessing” his candidacy, his next move still seemed a mystery. His campaign manager had promised that the Dayton speech would include an outline of Cain’s “strategic reassessment” of the campaign.

But instead, the candidate gave a fairly standard, upbeat stump speech, saying at one point: “I want to be president.”

Later in the day in Columbus, Cain was asked whether he intends to stay in the race for the long haul. “Still reassessing and reevaluating,” he said, adding he will decide in “several days.”

Cain has not budged from his denials that there was anything improper about his relationship with Ginger White, who said that she and the married candidate had carried on a long affair.

At a Republican Governors Association meeting in Orlando, Cain’s handling of the latest allegations drew criticism.

Mississippi Gov. Haley Barbour made clear that he does not think Cain’s campaign has dealt with the allegations effectively. He urged Cain to put all the facts on the table when the first allegations of sexual harassment came to light. “I don’t know if all the facts are out or not,” the governor said Wednesday.

Cain’s way of dealing with criticism appeared in his first moment in the national spotlight, when he questioned President Bill Clinton during a 1994 town hall meeting on health-care reform. Cain, then the chief executive of Godfather’s Pizza, told Clinton that his plans for expanding health insurance would drive up his operating costs.

Clinton wondered whether it would really cost that much. Couldn’t Cain just raise the price of pizza? “I’m a satisfied customer. I’d keep buying from you,” the president said.

The audience laughed and clapped at a slice of vintage Clinton: wonky details and lowbrow tastes.

What followed — though no one knew it at the time — was vintage Cain.

“With all due respect, your calculation on what the impact would do, quite honestly, is incorrect,” Cain responded. He explained how health-care costs would increase more than Clinton had predicted.

Finally, Clinton, trying to move on, asked Cain to send his figures to the White House.

This year, Cain used the same kind of flat rejection to deal with concerns about his 9-9-9 plan. In debates, moderators asked him about reports that the plan — a 9 percent corporate income tax, a 9 percent personal income tax and a 9 percent national sales tax — might raise taxes on many Americans and deliver less revenue than the current system.

Cain rejected the ideas out of hand. They were wrong, he said.

But then, soon afterward, Cain announced a new wrinkle in his plan: For the poorest Americans, he said, the proposal would be “9-0-9,” with no personal income tax required.

Cain also had to qualify his denial of the first sexual harassment allegations. In that case, his story changed the same day: He first said he was unaware of any financial settlement with one of his accusers. Then, later, he said he was, and described the gesture that he said was the basis of the accusation.

Cain’s attorney responded to the most recent accusation, involving White, with a more nuanced statement: He didn’t deny that it happened, but instead argued that the issue is private.

“This is not an accusation of harassment in the workplace. This is not an accusation of an assault,” attorney Lin Wood said.

Cain, however, issued a denial, telling CNN’s Wolf Blitzer that there had been no affair, no sexual relationship. “I don’t have anything to hide,” he said.

Gloria Cain, the candidate’s wife, seemed to indicate that Herman Cain had been equally forceful when she asked him about the harassment accusations. She described that conversation in an interview with Fox News Channel’s Greta Van Susteren this month, before the latest accusation.

“I wanted to know, ‘Are there any accusations — do you remember any of these people? Do you remember anything happening that was considered sexual harassment, or what?” Gloria Cain said. “He kept saying no.”

Somashekhar reported from Dayton and Columbus, Ohio. Staff reporters Rosalind S. Helderman in Manchester, N.H., and Dan Balz in Orlando contributed to this report.