THE WOODLANDS, Texas » If Herman Cain has been less than clear about exactly what happened during his tenure as head of the National Restaurant Association in the late 1990s, when he was accused of sexual harassment, he is being perfectly clear about how he intends to conduct himself now.

"We’re getting back on message, end of story," he said here in a suburb north of Houston on Saturday night after a debate with Newt Gingrich that ended up being more of a Tea Party pep rally than a clash of ideas. At no point during the nearly three-hour event, a fundraiser that began with cocktails, did Cain address what had consumed his campaign the previous week.

"Don’t even go there," he warned reporters who clamored to ask him at least one question after the event.

But Cain’s efforts to move past the story were thwarted Sunday by what may be a sign of things to come. One of his opponents for the Republican presidential nomination, Jon M. Huntsman Jr., and an influential Republican leader, Gov. Haley Barbour of Mississippi, used appearances on a Sunday morning talk show to urge Cain to be more forthcoming in responding to the accusations.

"Legitimate questions have been raised," said Huntsman, a former governor of Utah.

Cain has built his reputation — and won over hordes of conservative supporters — on being a folksy and straight-talking former pizza executive, an alternative to his rivals with their years of political experience. But his recent denials and evasions threaten to become a turning point, or at least a midcourse correction, on his unlikely but so far thriving campaign for the presidency.

The very qualities that endeared Cain to so many conservatives appear to be undercutting his chances, as his campaign struggles to respond to the sexual harassment accusations and as new questions are raised about the candidate’s management style, one of his central selling points. Cain, inexperienced on the national political stage, has stumbled repeatedly since Politico broke the story of the accusations a week ago. He has issued an avalanche of confusing and often contradictory statements, lashing out at his rivals and ultimately blaming the news media for reporting the news.

"His base is skeptical of the allegations," said Steve Schmidt, a Republican strategist. "However, he will have to get it behind him sooner rather than later. I suspect this week will be the key week on the issue, and then it will die. Of course, that depends on what the accusers are allowed to say. It continues to be fun to watch."

Cain told reporters after the debate Saturday that instead of asking him questions, they should read a copy of what he called "the journalistic code of ethics." And he has not budged on his insistence that he will not address specifics of the accusations.

Until Sunday, his Republican opponents were giving him the benefit of the doubt for the most part, and had generally refrained from directly taking him on concerning the accusations. But Huntsman, appearing on the NBC News program "Meet the Press" signaled that was no longer the case when he said, "It’s up to Herman Cain to get the information out and get it out in total." And Barbour, who also was on "Meet the Press," said, "People need to know what the facts are." Such comments could undercut Cain’s case that the accusations were stirred up by a left-wing news media intent on destroying his candidacy.

Still, polls released late last week suggested that the crisis was not eroding Cain’s standing as a top-tier candidate who was running neck and neck with Mitt Romney, the former governor of Massachusetts. J.D. Gordon, a spokesman for Cain, said the campaign had raised $6.7 million since Oct, 1, effectively tripling what it had collected during the entire summer. He said the campaign staff had grown last week to 65, up from 30 paid workers at the end of the summer.

But a new Reuters/Ipsos opinion survey released on Sunday found that damage has been done. The survey, which involved 1,007 adults who were interviewed online, found that Cain’s favorability rating among Republican voters had declined significantly in the past week, from 66 percent to 57 percent.

The Cain campaign did not respond on Sunday to a request for comment about its strategy. But, judging from the lack of any public campaign events over the next several days, Cain is likely to be spending time behind closed doors preparing for the next debate, on Wednesday, among the large field of candidates. The debates have, so far, been an opportunity for Cain to shine, highlighting his capacity for making quick and catchy remarks while promoting his simple policy prescriptions, like the "9-9-9" flat tax plan. But it is unlikely that he will be able to evade questions about the harassment accusations or make light of them should they arise in the debate, especially if more of his rivals use the moment to attack over an issue that has dominated chatter about the Republican field.

Simply allowing time to pass might not be the best strategy.

"Bad news is not like fine wine," Barbour said, paraphrasing a quote from former Secretary of State Henry A. Kissinger. "It doesn’t improve with age."