Story highlights Seven of the top GOP presidential candidates faced off in Las Vegas

Jon Huntsman decided to boycott Nevada and instead will campaign in New Hampshire

Front-runners Cain, Romney and Perry came under frequent attack

Romney and Perry trade sharp accusations

Tuesday night was fight night in Las Vegas.

Seven Republican presidential candidates clashed sharply over issues such as illegal immigration, taxes and health care at a presidential debate in Nevada sponsored by CNN and the Western Republican Leadership Conference.

But it was the three Republican front-runners -- former Godfather's Pizza executive Herman Cain, former Massachusetts Gov. Mitt Romney and Texas Gov Rick Perry -- who came under frequent attack.

The long-standing bad blood between Romney and Perry boiled over in the debate's first hour as the two GOP heavyweights traded harsh accusations and showed flashes of anger.

Romney laughed in Perry's face when the Texan criticized his rival for hiring illegal immigrants to work on his lawn, a controversy uncovered by The Boston Globe during Romney's first presidential bid in 2008.

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"Mitt, you lose all of your standing, from my perspective, because you hired illegals in your home, and you knew about it for a year," Perry said, turning straight to Romney. "And the idea that you stand here before us and talk about that you're strong on immigration is on its face the height of hypocrisy."

When Romney tried to respond, Perry refused to let him answer.

"You get 30 seconds," Romney said, looking to moderator Anderson Cooper. "This is the way the rules work here, is that I get 60 seconds and then you get 30 seconds to respond. Right? Anderson?"

Perry interrupted: "And they want to hear you say that you knew you had illegals working at your ... "

"Would you please wait?" a frustrated Romney shot back. "Are you just going to keep talking?"

"Yes, sir," Perry said.

An exasperated Romney tried to rise above the squabble.

"You have a problem with allowing someone to finish speaking," Romney said. "And I suggest that if you want to become president of the United States, you have got to let both people speak. So first, let me speak."

Romney fired back that Perry failed to secure the Texas border and again raised questions about his support for a law that granted in-state college tuition to the children of illegal immigrants.

"Texas has had 60% increase in illegal immigrants in Texas," Romney charged. "If there's someone who has a record as governor with regards to illegal immigration that doesn't stand up to muster, it's you, not me."

Perry's debate performance was, by far, his feistiest to date.

After surging to the top of Republican polls on joining the presidential race in August, Perry saw his standing slip among GOP voters after a series of lackluster debate showings.

But it was not clear as the debate concluded Tuesday whether Perry's aggressive tack would hurt him or help him.

A seemingly Romney-friendly audience in Las Vegas booed when Perry turned up the heat, and after the debate, one of Romney's senior advisers claimed that Perry only hurt himself by going so negative.

"Rick Perry came in to kill Mitt, but he killed himself," Romney adviser Eric Fehrnstrom said in the post-debate spin room.

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Ray Sullivan, Perry's communications director, claimed victory and called Romney a "slick guy" who will "change positions on a dime."

"He is back to running again," Sullivan said of Perry. "This is a campaign that is in for the long haul."

Cain, meanwhile, was at the center of a pile-on as the debate began.

His GOP rivals took turns picking apart his "9-9-9" plan to reform the United States tax code.

The plan would throw out the current tax system and implement a 9% corporate income tax rate, a 9% income tax rate and a 9% national sales tax.

The other six Republicans on stage -- who have watched Cain soar to the top of the polls in recent weeks thanks to his straightforward message and outsider image -- were united in calling the tax plan simplistic and risky.

"There are much more complexities than Herman lets on," said former House Speaker Newt Gingrich.

Texas Rep. Ron Paul called the plan "dangerous" and said it would increase taxes on low-income citizens.

Perry told Cain that voters "are not interested in 9-9-9; what they are interested in is flatter and fairer."

"I will bump plans with you, brother, and we will see who has the best idea about getting this country working again," Perry said. "It's not going to fly."

Romney said Cain's plan would add federal taxes on top of state taxes.

Cain said his plan would not raise taxes on poor people and said his opponents were misrepresenting his plan.

"The reason my plan is being attacked so much is the lobbyists accountants and politicians. They don't want to throw out current tax code and replace with something that's simple and fair," Cain responded.

The former businessman also stumbled when the debate turned to topics like immigration and foreign policy.

Just hours after telling CNN's Wolf Blitzer that he would consider negotiating a prisoner swap with al Qaeda, Cain denied that he had said any such thing.

He changed his answer after the debate in a follow-up interview with Cooper and said he would not negotiate with terrorists.

"I misspoke," Cain said. "Because I didn't, you know, things are moving so fast, I misspoke. I would not do that. I simply would not do that."

They were joined on the stage in Las Vegas by former Pennsylvania Sen. Rick Santorum and Minnesota Rep. Michele Bachmann, who also attacked the Cain plan.

Former Utah Gov. Jon Huntsman chose to boycott the debate because of a dispute between Nevada and New Hampshire over the GOP primary calendar.

Huntsman is staking his campaign on a win in New Hampshire and held a town hall there Tuesday night instead.

That left more time for the rest of the field to make their cases -- and to take aim at the front-runners.

Santorum called into doubt Romney's credibility on the matter of repealing President Barack Obama's health care plan because Romney passed a similar plan in Massachusetts.

"You just don't have credibility, Mitt, when it comes to repealing Obamacare," Santorum said. "You are -- you are -- your plan was the basis for Obamacare. Your consultants helped Obama craft Obamacare. And to say that you're going to repeal it, you just -- you have no track record on that that -- that we can trust you that you're going to do that."

The exchange rapidly descended into a shouting match as Santorum refused to let Romney respond.

Eventually, Romney said he would "absolutely not" impose his Massachusetts plan on the rest of the country.

Bachmann, meanwhile, took aim at the Cain tax plan and said it would create a de facto value added tax.

But she repeatedly tried to refocus the debate on Obama instead of her GOP opponents.

"We need to repeal Obamacare, repeal the Jobs and Housing Destruction Act known as Dodd-Frank," she said. "President Obama's plan has been a plan for destruction for this economy and failure. I plan to change that."

The candidates were also asked about Robert Jeffress, the controversial Baptist pastor and Perry supporter who recently said the Jesus Christ Church of Latter-day Saints is a "cult."

They seemed to agree that while a candidate's religion is a legitimate topic in a campaign, the freedom to worship as one chooses is enshrined in the Constitution.

"The concept that we select people based on the church or the synagogue they go to, I think, is a very dangerous and enormous departure from the principles of our Constitution," Romney said.

Perry, asked if he would repudiate the Jeffress comments, said he already had.

"I said I did not agree with Pastor Jeffress' remarks," he said. "I don't agree with them. I can't apologize any more than that."

Romney accepted the answer.

"That's fine," he said.