Washington (CNN) -- Herman Cain doesn't want to talk about the sexual harassment allegations dogging his bid for the Republican presidential nomination, but plenty of other folks weighed in on Sunday.
Those opposing the former business executive's campaign called for keeping the issue alive, saying the necessary scrutiny of presidential candidates requires Cain to answer all questions about what happened when he headed the National Restaurant Association in the late 1990s.
"It's up to Herman Cain to get the information out and get it out in total," Jon Huntsman, the former Utah governor running far behind Cain in polls so far, told NBC's "Meet the Press" program. "That's important because we've got some real issues to discuss in this campaign, and this is taking all the bandwidth out of the discussion. So we're not able to talk about jobs. We're not able to talk about our position in the world. And that hurts."
Conservatives, angered by the media attention to the potentially fatal accusations for the tea party favorite's campaign, argued that the lack of specifics -- with no public disclosure yet of an accuser's name or specific offense alleged -- showed it was all more circus than substance.
"Until something comes out that's concrete, I think it is politics as usual," retiring Sen. Kay Bailey Hutchison, R-Texas, told CNN's "State of the Union."
Cain made clear his wishes, scolding reporters who asked about the issue following a debate with fellow conservative Newt Gingrich on Saturday night in Texas.
"Don't even go there," Cain told one questioner who'd asked about the allegations. Asked again later, he responded: "What I'm saying is this -- we are getting back on message, end of story. Back on message. Read all of the other accounts, where everything has been answered -- end of story."
Cain has denied allegations, first reported October 30 by Politico, that he sexually harassed two women who worked at the restaurant association, and that both left the organization after getting either settlements or severance pay, depending on who is telling the story.
On Friday, a lawyer for one of the women released a statement saying she stood by her claims against Cain. However, the woman has so far refused to allow her identity or specifics of her allegations to be made public.
The apparent reluctance of Cain's accuser to tell all could work in the candidate's favor by creating a public perception the accusations lack substance, said Mississippi Gov. Haley Barbour, an influential figure in Republican politics.
"If that's the truth, then what Herman Cain needs to do is push very hard to make those facts plain," Barbour said on NBC.
Republican consultant Liz Cheney, the daughter of the former vice president, said the unending media attention on the story created even more pressure.
"When you're in the middle of a feeding frenzy like this, it's often difficult to move on," Cheney said on the CBS program "Face the Nation." "But I think you have to have the confidence to know at the end of the day, you know, so long as we don't see more damaging facts come out, this is not the issue that's going to decide the election."
To Rep. Darrell Issa, a California Republican backing former Massachusetts Gov. Mitt Romney in the GOP race, Cain is undergoing a difficult transition from private business figure to public politician.
"To go directly from being a businessman, without substantial time in the government arena, both the vetting and the knowledge of it, is really hard," Issa told NBC. "It's virtually impossible" and in Cain's presidential quest, may be "a bridge too far."
Former New Mexico Gov. Bill Richardson, a strong Democratic Party voice, suggested Cain's troubles were only part of the problem for Republicans on women's issues.
"I think what you're seeing is a huge assault on women's rights in the Republican parties, and an extreme right-wing that has taken over that is going to make it very difficult for anybody in a general election in the Republican Party to be a centrist," Richardson said on NBC.
Despite the week of uproar over the accusations, Cain's campaign reported a spike in donations, while polls have yet to determine any significant effect on his support.
Gary Bauer of the conservative American Values non-profit organization told CNN that the lack of specifics in the Cain accusations has prompted public skepticism.
"We don't know exactly what he's allegedly done, and we don't have the names of any accusers, so I'm not surprised at all that it hasn't moved his support and it certainly hasn't changed my opinion of him," Bauer said. "I hope we don't get to a point in this country where anonymous allegations can ruin a decent man's career. I don't think we are. And I hope we never get there."
On the same program, Rev. Jim Wallis of the progressive Christian group Sojourners said the question involves the connection between personal integrity and public leadership.
"The real issue here beyond Cain is what a candidate's moral compass is and how that shapes their policy views," he said.
CNN's Shannon Travis contributed to this report.