"The American people deserve better than someone being tried in the court of public opinion due to unfounded accusations," Cain said. "I value my character and my integrity more than anything else. And for every one person that comes forward with an unfair accusation there are probably, there are thousands who come forward and say none of that ever happened with Herman Cain."
So far, Cain's rivals have refrained from attacking him directly, not wanting to risk a backlash from his supporters.
Romney, a former investment banker and former governor of Massachusetts, was asked whether he would hire Cain as a CEO with "character" questions hanging over him.
"Herman Cain is the person to respond to these questions," Romney said. "He just did."
The scandal threatened to overshadow a discussion on economic issues. Michigan's economy is distressed - with an 11.1 percent unemployment rate and a dependence on an auto industry that was on the verge of collapse before a federal bailout in 2009.
All eight of the Republican candidates on the stage opposed the bailout that rescued General Motors and Chrysler, preserving hundreds of thousands of jobs at the automakers themselves and at companies that supply them.
Romney grew up in Michigan, where his father was governor and chief executive of the now-defunct American Motors Corp. He was asked early on about his opposition to the bailout.
The federal plan gave the United Auto Workers a controlling share in GM and forced Chrysler to merge with Italian automaker Fiat, Romney said.
"We would have had a private-sector bailout - private-sector restructuring and bankruptcy with the private sector guiding [it]... as opposed to what we had with the government playing its heavy hand," he said.
Voting in the 2012 presidential nominating process begins in Iowa in a little over six weeks.
Romney and Cain were joined at the debate by Texas Gov. Rick Perry, former House Speaker Newt Gingrich of Georgia, Minnesota Rep. Michele Bachmann, former Pennsylvania Sen. Rick Santorum, former Utah Gov. Jon Huntsman, and Texas Rep. Ron Paul.
Perry proposed to audit every federal regulation promulgated since 2008.
"If it's not creating jobs, get rid of it," he said. "We need to go out and stick a big ol' flag in the middle of America that says we're open for business again."
Contact politics writer Thomas Fitzgerald at 215-854-2718 or firstname.lastname@example.org or @tomfitzgerald on Twitter. Read his blog, "The Big Tent," at www.philly.com/BigTent.