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“I hope I am the Tim Tebow of the Iowa caucuses,” he said.

Rep. Ron Paul, a Texas Republican who is the latest to see positive movement in the polls, said he is not worried about electability next year.

“Fortunately for the Republican Party this year, probably anybody up here could probably beat Obama,” he said. “The challenge isn’t all that great on how we’re going to beat Obama. I think he’s beating himself.”

Mr. Paul, though, faced heavy criticism from his fellow candidates for saying he doubted Iran was working toward a nuclear weapon, and saying if it was, it would be understandable given their geography. He said some American officials appear to be laying the ground for war.

“You know what I really fear about what’s happening here? It’s another Iraq coming. It is war propaganda going on,” he said. “To me the greatest danger is that we will have a president that will overreact, that we will soon bomb Iran.”

He later said he didn’t want Tehran to get an atomic bomb, but said the solution was not sanctions or war, but rather a retrenchment of U.S. military positions throughout the world.

The most pointed exchanges came between Mr. Gingrich on the one hand and and Mrs. Bachmann and former Sen. Rick Santorum of Pennsylvania on the other, with the latter candidate implying Mr. Gingrich was not a reliable conservative when he was House speaker in the mid-1990s.

“If you were a conservative and you had an issue that you wanted to get voted on and you wanted to get done in the United States Senate, you came to Rick Santorum, because I was the guy fighting for the conservative cause when it was popular and when it was unpopular,” he said.

“The speaker had a conservative revolution against him when he was the speaker of the House. I had conservatives knocking down my door, because I was the effective advocate for the principles that they believed in.”

Mrs. Bachmann also questioned Mr. Gingrich’s pro-life bona fides on the grounds that he said he would campaign for Republicans who opposed bans on partial-birth abortion, a charge that Mr. Gingrich dismissed by saying he opposes party purges and by pointing to pro-life groups having given him a 98.5 percent rating as a legislator.

Under that scrutiny from both his fellow candidates and the Fox News panelists, Mr. Gingrich didn’t back down from his stances, including defending his plan to try to force federal judges to curtail their more adventurous decisions — up to abolishing entire appeals courts over decisions that he said pervert the Constitution.

“I would be prepared to take on the judiciary if in fact it did not restrict what it was doing,” he said.

The debate — the last one scheduled before Iowa voters hold their Jan. 3 caucuses — marked the last, best chance for the candidates to appeal to the broad swath of voters with any depth.

From here on out, the battle will be fought in 30-second television ads that reach broadly but usually deliver little substance, or town hall meetings that deliver on depth but are limited to several dozen people at a time.

A new Rasmussen Reports poll released Thursday showed Mr. Romney taking a 3 percentage point lead in Iowa from Mr. Gingrich, who a month ago held a 13-point lead. Other recent polls still show Mr. Gingrich on top, with Mr. Romney and Mr. Paul competing for second place.

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