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Republican presidential hopefuls on Thursday night didn't allow President Obama's widely-praised operation that killed Usama bin Laden this week to deter them from attacking his foreign policy or blaming his domestic policies for high gas prices and the fragile economy recovery.

During the first debate of the 2012 election season, former Minnesota Gov. Tim Pawlenty congratulated Obama for capturing the world's most wanted terrorist nearly 10 years after the Sept. 11 attacks.

"I tip my cap to him in that moment," he said. "But that moment is not the sum total of America's foreign policy. He's made a number of other decisions relating to our security here and around the world that I don't agree with."

Pawlenty cited Libya as one example, saying he didn't agree with Obama's decision to defer to the United Nations on how to deal with Muammar Qaddafi's violent crackdown on rebels.

Former Pennsylvania Sen. Rick Santorum said the only thing Obama has done right in his foreign policy is continue President George W. Bush's policies.

"The decision he made with Usama bin Laden was a tactical decision," he said. "It wasn't a strategic decision. The strategic decision was made by President Bush to go after him. What President Obama has done on his watch, the issues that have come up while he's been president, he's gotten it wrong strategically every single time."

Pawlenty and Santorum were among the five participants seeking to prove themselves to be more than the party's B-team as they try to catapult their White House bids into the national spotlight.

Fox News and the South Carolina Republican Party  sponsored the debate that also featured Texas Rep. Ron Paul, former New Mexico Gov. Gary Johnson and businessman Herman Cain.

FULL COVERAGE: GOP Presidential Debate

They are the only willing candidates who met the sponsors' criteria to participate: forming a presidential exploratory committee, filing state GOP paperwork and paying $25,000 to get on the state primary ballot.

The GOP field is still taking shape, with about a dozen Republicans considering a White House bid or taking initial steps toward full-fledged campaigns. Among the notable absences were Sarah Palin, Donald Trump, Mitt Romney, Mike Huckabee and Newt Gingrich.

They missed out on a chance to weigh in on the biggest issues of the day, including whether to release a photo of bin Laden's corpse, something that Obama has said he won't do. But four of the five participants said they would release the photo. Cain was the only one who opposed it.

Three participants said they support waterboarding on a case-by-case basis. It is a sort of simulated drowning that Obama has deemed torture and banned but that others some believe led to the capture of bin Laden. Paul and Johnson said they didn't support waterboarding.

"Because you don't achieve anything," Paul said.

But Santorum shot back, "Well that's just simply not true, Ron. I mean the fact is that some of this information that we have found out that led to Usama bin Laden actually came from these enhanced interrogation techniques."

At one point, Johnson, a libertarian-leaning Republican who backs gay rights and legalizing some drugs, cried foul over not getting as many questions as his fellow debaters. Fox News' anchor Bret Baier said the moderators would be "fair and balanced" with the questions.

Paul, the Libertarian Party presidential nominee in 1988, received thunderous applause after most of his answers. His 2008 GOP-run inspired the modern Tea Party movement, and he planned to address the marathon South Carolina Tea Party rally after Thursday's debate.

Asked to reconcile his support for the Defense of Marriage Act, a federal law banning gay marriage, and his statements saying the government shouldn't dictate who can get married, Paul said the law protects states' rights.

"The Defense of Marriage Act was really designed to make sure that the states have the privilege of dealing with and the federal government can't impose their standards on them," he said.

The participants agreed that the economy would be the president's biggest weakness in the election.

"We're on the verge of a financial collapse unless we balance the budget, and that means some really, really tough decisions," Johnson said.

Cain, a former Federal Reserve banker and CEO of Godfather's Pizza, criticized Obama's energy plan, which he blamed for rising gas prices.

"If the world market believed that we were serious about energy independence and we were going to utilize all of our existing resources, the speculators wold stop speculating up and they would speculate down until we get our own oil out of the ground," he said to roaring applause.

Paul outlined his "theory" that Americans "vote from their bellies."

"Because it's whether they're hungry, or have jobs or need things, that's why they vote," Paul said. "And we're in big trouble. Prices are going up. Unemployment is continue to go up. And we have not had the necessary correction for the financial bubble created by our Federal Reserve system."

Before Thursday's debate, Pawlenty zinged those rivals who chose to skip the debate.

"One of the things about leadership is that you've got to show up," he said. "And if you want to be president of the United States you've got to make a case to the American people that Barack Obama needs to be dismissed from his position."

Fox News' Carl Cameron contributed to this report.