Rochester, Michigan (CNN) -- Appearing Wednesday in a presidential debate in Michigan focused primarily on economic matters, Republican Herman Cain again faced down questions about the sexual harassment scandal that has engulfed his campaign and the Republican race for the White House.
"Why should the American people hire a president if they feel there are character issues?" Cain was asked by one of the moderators, Maria Bartiromo of CNBC, in the early moments of the debate.
The crowd at Oakland University in suburban Detroit loudly booed the question, but Cain maintained a straight face and denied that he has acted inappropriately around any woman.
"The American people deserve better than someone being tried in the court of public opinion," Cain answered. "I value my character and my integrity more than anything else. One person comes forward with a false accusation, and there are probably thousands who would say none of that activity came from Herman Cain."
Though polling indicates that Republicans have some concerns about the scandal, Cain said Americans are "still very enthusiastic about my candidacy" and have responded with a flood of campaign donations.
When the other moderator, John Harwood, asked Republican front-runner Mitt Romney if he would fire Cain knowing the allegations, he was also booed.
"Would you keep Herman Cain as CEO knowing what you know?" Harwood asked.
Romney, who called the harassment allegations "disturbing" and "serious" on Tuesday, did not answer.
"Herman Cain is the person to respond to these questions," Romney said.
The debate, sponsored by the Michigan Republican Party and CNBC, was the ninth such forum of the presidential campaign.
Eight candidates participated. With Cain and Romney were: Texas Gov. Rick Perry, former House Speaker Newt Gingrich, Texas Rep. Ron Paul, former Utah Gov. Jon Huntsman, former Pennsylvania Sen. Rick Santorum and Minnesota Rep. Michele Bachmann.
The contenders were also asked about the European debt crisis, the bailout of the American auto industry, the 2008 Wall Street bailout and the tax code.
The candidates appeared to agree that the government should not try to bail out or "have a stake" in faltering European economies, even with investor confidence in Greece and Italy plummeting and the debt crisis threatening American markets.
"There will be some who say here that banks in the U.S. that have Italian debt, that we ought to help those, as well," Romney said. "My view is no, no, no. We do not need to step in to bail out banks either in Europe or banks here in the U.S. that may have Italian debt."
Romney also doubled down on two of his more controversial positions that Democrats have seized on: his opposition to the government bailout of the auto industry and his criticism of federal efforts to modify home loans and prevent foreclosures.
The former Massachusetts governor has said the health of the housing market should rise and fall with the market, without government intervention.
The night was not marked by the kind sharp clashes between the candidates that played out in previous debates.
Instead, the focus remained largely on financial matters as the candidates issued familiar promises to reduce the size of government, reform entitlements and roll back taxes and regulations.
But one major candidate managed to inflict a serious and perhaps fatal wound to his presidential hopes -- and without help from his rivals.
Perry, whose past debate performances raised questions about his readiness for the national stage, stumbled badly in the course of naming three federal agencies he would eliminate.
In the course of promising to repeal job-crushing government regulations, Perry said he would eliminate three government agencies. But in an excruciating minute-long answer full of pauses, he could not remember the third.
"Commerce, Education, and the -- what's the third one there? Let's see," Perry said, looking puzzled and searching his notes.
When he finally named the Environmental Protection Agency after another candidate mentioned it as a possibility, Harwood followed up.
"Seriously, is the EPA the one you were talking about?" he asked.
"No sir, no sir. We were talking about the agencies of government -- the EPA needs to be rebuilt," Perry responded. "There's no doubt about that."
"But you can't name the third one?" Harwood pressed.
Finally, Perry gave up.
"Commerce and, let's see," he said. "I can't. The third one, I can't. Sorry. Oops."
The moment was so problematic that the Perry campaign made the rare decision to bring the candidate himself into the spin room to explain himself. It turned out the agency he was searching for was the Department of Energy
"I'm sure glad I had my boots on because I sure stepped in it out there," Perry told a pack of reporters. "The bottom line is, I may have forgotten Energy, but I didn't forget my conservative principles."
Romney adviser Eric Fehrnstrom let the moment speak for itself.
"There is nothing I could say that could darken the night that Rick Perry had," he told reporters. "I would prefer to talk about Gov. Romney's performance."