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The debate was an unwieldy affair as moderator Wolf Blitzer jumped around among the eight candidates, meaning some of them never answered major questions, such as whether they would authorize an attack on Iran or aid an Israeli strike.

But across the two hours, different versions of conservatism emerged over the scope of powers the federal government should have to combat terrorism.

Mr. Gingrich and Mr. Perry said they would seek to strengthen the Patriot Act to give the president more powers to try to stop future attacks.

Mr. Romney said there needs to be a distinction between criminal law and the rules of war.

“For those that understand the difference between the two, they understand we need tools when war is waged domestically,” Mr. Romney said.

Mr. Romney took his strongest stand of the debate in opposing the automatic defense spending cuts that are now slated to take effect in 2013 after the deficit supercommittee failed Monday to reach a $1.2 trillion debt deal.

But Mr. Paul, a Texas Republican who has emerged as a chief defender of limited intervention and constitutional liberties, said there’s plenty of cutting room.

“It seems like nobody cares about the budget. We’re in big trouble, and nobody wants to cut anything,” he said.

Also taking part in the debate were former corporate CEO Herman Cain, former Utah Gov. Jon Huntsman Jr. and former Sen. Rick Santorum of Pennsylvania.

With Iowa’s first-in-the-nation caucuses less than six weeks away, there’s little time left for candidates seeking to make a move into the top tier, which currently consists of Mr. Romney, Mr. Gingrich and to a lesser extent Mr. Cain and Mr. Paul.

Mr. Gingrich is the latest to surge in polls. A new Quinnipiac University poll released Tuesday showed him atop the leader board nationally.

But the poll also held some warning signs for Mr. Gingrich that suggested his well-documented political past and extramarital affairs could come back to haunt him in the nomination race, leaving him to face the same sort of fate as Mrs. Bachmann, Mr. Perry and Mr. Cain — all of whom enjoyed stints at the front of the pack.

Mr. Romney, meanwhile, is doubling down on what appears to be a general election strategy aimed at making this a race between him and Mr. Obama. On Tuesday, he ran full-page advertisements in New Hampshire’s biggest newspapers and released a new television ad, in which he contended the policies of Mr. Obama have failed the nation.

The event Tuesday night in Washington marked the 11th debate since summer. It was the second debate this month to focus on foreign policy and the first time the major candidates stood on the same stage since the 12-member bipartisan congressional supercommittee tasked with coming up with $1.5 trillion in tax increases and/or spending cuts over the next 10 years announced that it had failed in its mission.

Now, under the deal Mr. Obama and congressional leaders agreed to over the summer, automatic cuts totaling $1.2 trillion, split between defense and domestic spending, are set to go into effect in 2013.

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