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Republican presidential contender Herman Cain on Saturday vowed to answer no more questions about decade-old sexual harassment allegations and blamed journalists for the claims that have dogged his campaign.

Growing agitated with reporters after a one-on-one debate with rival Newt Gingrich, the former business executive suggested the reporters who asked questions about the allegations were unethical. Asked if he planned to never answer questions about the incidents, he was certain.

"You got it," he snapped, even as the allegations leave plenty of doubts about Cain's candidacy.

A lawyer for one of Cain's accusers said Friday that his client had filed a complaint "in good faith" against Cain in the 1990s for "several instances of sexual harassment" and had received a financial settlement.

Attorney Joel Bennett suggested Cain wasn't telling the truth in his repeated denials of the incidents that allegedly took place while the Georgia businessman headed the National Restaurant Association.

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Cain repeatedly has denied ever sexually harassing anyone, and his campaign said it was "looking to put this issue behind us." Advisers had hoped Saturday night's debate here near Houston would help do that.

Tea party organizers explicitly limited to the discussion to Social Security, Medicare and Medicaid.

Gingrich, however, gave Cain an opportunity to address the allegations with an open-ended question about what has surprised him about running for president.

Cain didn't hesitate: "The nit-pickiness of the media," he said.

"It is the actions and behavior of the media that have been the biggest surprise," he said, his voice rising.

"There are too many people in the media who are downright dishonest. ... They do a disservice to the American people," Cain said, bringing the room to its feet.

Gingrich had nothing to gain by raising allegations of improper sexual behavior by one of his rivals. The former House speaker from Georgia has been divorced twice and married three times, including to his current wife with whom he had an affair while married to his second wife.

Yet the moment gave Cain another opportunity to decry the media, whom he has blamed for the allegations becoming public.

"If I were running this campaign the way the pundits thought I ought to be running this campaign, I would have dropped out in August," Cain later told reporters.

"When people get on the Cain train, they don't get off."

A Washington Post-ABC News survey taken after the allegations emerged last Sunday showed Cain and former Massachusetts Gov. Mitt Romney running almost even atop the field, with most Republicans dismissing the harassment allegations. Seven in 10 Republicans say reports of the allegations don't matter when it comes to picking a candidate.

But in a sign of the possible danger ahead, the poll found that Cain slipped to third place among those who see the accusations as serious, and Republican women were significantly more likely than men to say the allegations make them less apt to support the businessman.

The questions show no sign of letting up.

When reporters tried to ask about the allegations following Saturday's debate, Cain interrupted.

"Don't even go there," Cain said before the reporter from The Washington Post could finish his question.

"Can I ask my question?" the reporter said.

"No," Cain snapped.

"Please send him the journalistic code of ethics," Cain instructed his chief of staff, Mark Block.

As he left the press conference, he began to offer an answer.

"If you all just listen for 30 seconds, I will explain this one time," Cain said.

He then immediately recanted.

"I was going to do something that my staff told me not to do and try to respond, OK?" he said. "We are getting back on message. End of story. Back on message. ... Everything has been answered."

During the otherwise staid evening, Cain and Gingrich largely agreed with each other that Washington was too big and spending was too high during the $200-per-ticket event modeled after the 1858 debates between Abraham Lincoln and Stephen Douglas.

Those debates between rivals for a U.S. Senate seat from Illinois were sprawling discussions of substance that politicians hold up as models for civil discussions. Gingrich, a former history professor, lauds them during his campaign and has proposed a series of seven, three-hour debates with President Barack Obama.

The other candidates vying for the GOP nomination were invited; only Cain and Gingrich accepted the invitation.

Organizers said Saturday they were considering more head-to-head debates and planned to work with the remaining candidates to schedule them.

At several points, it gave both Cain and Gingrich an opportunity to make lengthy points on fiscal issues.

"Long-term projections about what a government program is going to cost have never been right," Cain said, projecting confidence as he sat side-by-side with the former House Speaker in high-back chairs.

"Name one," Cain challenged the audience with similar defiance he displayed all week as he fought to steady his political campaign.

Asked after the debate about the last seven days, Cain didn't hesitate: "I've had a great week. A great week."