Las Vegas -LRB- CNN -RRB- -- 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 . `` 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 . '' GOP debate takes negative turn 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 does n't stand up to muster , it 's you , not me . '' iReport : Give us your take on the candidates 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 . 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 . Truth Squad : Fact checking the GOP debate 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 do n'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 did n'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 do n'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 do n't agree with them . I ca n't apologize any more than that . '' Romney accepted the answer . `` That 's fine , '' he said . CNN 's Kevin Bohn contributed to this report .