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ROCHESTER, Mich. — Gov. Rick Perry of Texas emphatically declared at a Republican presidential debate Wednesday night that he would like to eliminate three government agencies. But as he began to explain, he could think of only two.

"Commerce, Education," Perry said, pausing for an uncomfortable moment and looking from side to side as he counted on his fingers and flipped through notes. As his rivals offered suggestions, a moderator asked if he could name the third agency. "I can't," he finally said, a sad look on his face.

"Oops," he said.

As Perry tries to revive his candidacy and present himself as a serious contender to Mitt Romney, Herman Cain and the rest of the Republican field, his lapse promised to be the most memorable moment of the two-hour debate on CNBC, an encounter otherwise dominated by polite exchanges over economic policy. It was not until several minutes later, when he received another turn, that Perry said: "By the way, that was the Department of Energy I was reaching for a while ago."

The Republican candidates seemed intent on trying to move beyond the distractions and quarreling that have dominated the campaign in recent weeks. They presented a unified front against government bailouts and offered sharp criticism of how President Barack Obama has handled the economy, but repeatedly declined to challenge one another.

The sexual harassment accusations against Cain, which have been hanging over his candidacy for the past 10 days, were raised only once during the debate. As a moderator asked him about the importance of character in presidential candidates, the audience jeered.

"The American people deserve better than someone being tried in the court of public opinion based on unfounded accusations," Cain said, drawing enthusiastic applause from the Republican crowd. "I value my character and my integrity more than anything else."

When Romney was asked whether he, as a businessman, would have allowed Cain to remain as a chief executive officer in light of the allegations, the audience hissed at the question. Romney paused and waited for the commotion to quiet.

"Herman Cain is the person to respond to these accusations," Romney said. "He just did. And the people in this room and around the country can make their own determination."

With that brief exchange, the candidates moved back to a wide-ranging economic conversation. They drew few distinctions with one another as they embraced Republican orthodoxy — less government intervention and more reliance on markets — while addressing bank bailouts, the nation's tax structure and declining home values.

Perry, who had struggled through each of his previous debates, initially seemed to be relaxed and prepared for a debate that was focused specifically on the economy. But in the second hour, he stumbled as he addressed the steps he said he would take to balance the budget by 2020.

"I will tell you, it is three agencies of government when I get there that are gone," Perry said. "Commerce, Education, and the — what's the third one there? Let's see."

As someone on stage suggested the Environmental Protection Agency, one of the moderators, John Harwood of CNBC, said, "Seriously, is the EPA the one you were talking about?"

"No, sir. No, sir," Perry said, trying to regain his thought. "Let's see. I can't. The third one, I can't. Sorry. Oops."

The two-hour debate Wednesday night was sponsored by CNBC and the Michigan Republican Party. The Republican nominating contest has been essentially frozen in place, with Romney and Cain showing the most strength in national and state polls. Yet Romney had come into the debate believing that his biggest rival is Perry.

Jon M. Huntsman Jr., the former Utah governor; Rep. Ron Paul of Texas; former Speaker Newt Gingrich; Rep. Michele Bachmann of Minnesota; and former Sen. Rick Santorum of Pennsylvania also were looking for a breakout moment at the debate that could prompt Republicans to take a second look before the first voting begins in less than two months.

The nation's hurting economy, along with the deep financial uncertainty in Europe, provided a backdrop for the first debate of the season to be held in the industrial Midwest. The state's unemployment rate of 11.1 percent, after an extensive loss of manufacturing jobs, and an epidemic of home foreclosures have made Michigan a crucible for a discussion of whether the government should intervene to prevent an economic collapse.

Yet Michigan is experiencing a revival compared with many parts of the country, with at least some of the jobs in the auto industry returning. Obama has visited Michigan nine times since taking office, hoping to use the state as an example of economic progress.

On a day when the stock market plummeted amid fears that Greek and Italian debt might bring European financial institutions to collapse, the candidates each rejected the idea that the United States should intervene to help, arguing that U.S. taxpayers should not be responsible for the missteps of foreign countries and companies and that the Obama administration's bailouts of banks here two years ago amounted to government overreach.

"My view with regards to the bailout — whether it was by President Bush or President Obama — is it was the wrong way to go," said Romney, the former Massachusetts governor, who grew up in Michigan.

Paul said European debt had to be "liquidated" to right the economy, while Huntsman said Europe's troubles presaged those that the United States would soon have if the president and Congress did not restrain government spending.