ROCHESTER, Mich. — Republican presidential candidates drew a bright line against government help for the private economy Wednesday night, whether it’s to bail out the U.S. auto industry at home or ease a debt crisis in Italy that could threaten the world economy.

“Europe is able to take care of its own problems,” said former Massachusetts Gov. Mitt Romney. “We don’t want to step in and try to bail out their banks and bail out their governments.”

“We are not going to pick winners and losers from Washington, D.C.,” added Texas Gov. Rick Perry, summing up a broad consensus among the candidates in a debate here.

The debate focused on the economy in an industrial state that’s been in an economic slump for a decade, but it’s more likely to be remembered for Perry’s stumbling. Perry, who fell from the top tier of candidates in most polls this fall after weak debate performances, struggled Wednesday after he said there are three government agencies “when I get there that are gone.”

Texas Rep. Ron Paul told him he needed five. Perry seemed flustered. He named the Commerce and Education departments but couldn’t come up with his own third target agency. The Environmental Protection Agency was suggested.

“EPA, there you go,” Perry said.

“Seriously, is the EPA the one you were talking about?” asked moderator John Harwood.

“No sir, no sir,” Perry said, explaining that the EPA “needs to be rebuilt.”

Perry tried again, citing the Education Department. He looked quizzically at the moderators. “Commerce and let’s see, I can’t. The third one, I can’t. Sorry. Oops,” Perry said. Later, he said he’d meant to cite the Energy Department.

The clash among eight GOP candidates at Oakland University, in suburban Detroit, was the first since accusations began to surface that businessman Herman Cain had engaged in aggressive sexual behavior toward four women in the past. He again flatly rejected all allegations, and won applause.

“The American people deserve better than someone being tried in a court of public opinion based on unfounded accusations,” he said to applause from the audience, “and I value my character and my integrity more than anything else.

“And for every one person that comes forward with a false accusation, there are thousands who would say none of that sort of activity ever came from Herman Cain.”

Romney, a former business executive, was asked whether he would retain a CEO who faced character questions of the sort dogging Cain.

“Herman Cain is the person to respond to these questions. He just did,” Romney said. “The people in this room and across the country can make their own assessment.”

The debate focused mostly on the economy, on a day when stock markets plummeted out of fears of a spreading debt crisis in Italy, the world’s seventh-largest economy.

Pressed on the looming European debt crisis, the eight candidates sounded a similar refrain against any direct U.S. aid to stem it.

Romney said he’d support international institutions such as the International Monetary Fund, but would provide no direct aid to banks in Europe to stop the crisis from spreading.

Paul said the U.S. should let debtors fail.

“You have to let it liquidate,” Paul said. “If you prop it up, you’ll do what we did in the Depression, prolong the agony …You’re going to perpetuate this for a decade or more.”

Government bailouts of the auto industry were equally unpopular. Romney, whose father George was an auto company executive and governor of this state from 1963 to 1969, has been under fire from Democrats for what appeared to be changing positions on government rescue of the auto industry during the 2008 economic collapse.

He said he’d preferred to let the auto industry go through bankruptcy reorganization on its own, rather than with taxpayer help and government direction.

“Whether it was by President Bush or President Obama, it was the wrong way to go,” he said.

Romney also was grilled about the perception that he often changes his views to fit the political mood.

“I’m a man of steadiness and constancy,” he said. “I’ve (been) married to the same woman for 25 – excuse me, I will get in trouble, for 42 years. I have been in the same church my entire life.”

The candidates repeated long-held views on taxes and health care, though former House Speaker Newt Gingrich protested having to describe his plans to revamp health care in 30 seconds.

Gingrich drew applause when he criticized media coverage of the Occupy Wall Street movement.