LAS VEGAS – Republican presidential candidates brawled Tuesday over Herman Cain’s 9-9-9 tax plan and Mitt Romney’s record on illegal immigration and health care, as rivals hammered the two top-tier contenders in the liveliest GOP clash of the 2012 campaign.

The sometimes-angry clash at the Venetian Hotel Resort Casino featured Texas Gov. Rick Perry accusing Romney, the former Massachusetts governor, of “the height of hypocrisy” on immigration. Romney scolded Perry for interrupting him and said Perry was “testy.” And candidates were sometimes difficult to understand as they talked over one another.

Cain, the Georgia businessman who surged to the top tier of national polls in recent weeks, was under fire for his plan to scrap the federal tax code and replace it with 9 percent taxes on individuals, businesses and sales.

“Middle-income people see higher taxes under your plan,” said Romney, one of several candidates to pile on Cain from the opening minutes of the two-hour debate.

“Reports are now out that 84 percent of Americans would pay more under his plan,” said former Sen. Rick Santorum of Pennsylvania. “You’re talking about major increases in taxes on people.”

Perry, whose poll numbers have tumbled after being perceived as having poor debate performances and who needed a strong showing Tuesday, joined the fray.

“You don’t need to have a big analysis to figure this thing out,” Perry said. The Cain tax would add a 9 percent sales tax in states such as Nevada, which already has a sales tax rather than an income tax, and in politically important New Hampshire, where voters are accustomed to paying no sales tax.

“I don’t think so, Herman,” Perry added. “It’s not going to fly.”

Cain brushed aside the torrent of criticism.

“It does not raise taxes on those making the least,” he said. “That simply is not true.”

But a new analysis from the Tax Policy Center, released late Tuesday afternoon, said the Cain plan would raise taxes on all taxpayers making less than $200,000, about 84 percent, while cutting taxes for higher incomes. The study found that those making more than $1 million would get an average tax cut of $455,000 from current rates.

Also sparking a lively battle was immigration, a particularly sensitive issue in Nevada and the states around it. Perry, defending his efforts to monitor the Texas-Mexico border, went after Romney.

“Mitt,” he said, “you lose all of your standing, from my perspective, because you hired illegals in your home and you knew about it for a year. 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.”

“Rick,” Romney shot back, “I don’t think I’ve ever hired an illegal in my life.”

Perry interrupted. Romney tried to speak. “I’m speaking,” Romney repeated three times.

Perry kept interrupting. “This has been a tough couple of debates for Rick, and I understand that,” Romney said. “And so you’re going to get testy.”

Perry kept pushing. The usually hard-to-rattle Romney was getting exasperated.

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

Romney offered the same defense he gave four years ago, when he was running for the GOP nomination, and former New York City Mayor Rudolph Giuliani made the same charge.

“No,” he said at the time, “I did not” hire an illegal immigrant.

Romney for several years used a lawn service at his home that employed undocumented aliens.
The campaign explained in 2007 that “Governor Romney hired a company, not the individuals who were not of legal status. The owner of the company was a legal immigrant who claimed that the workers were legal, though he did not request documentation.”

Romney, campaign officials said, had no knowledge of the legal status of the company’s employees.
Romney also found himself on the defensive Tuesday on another familiar topic: his support of a Massachusetts law that requires nearly everyone in the state to obtain health care coverage, considered a model for the 2010 federal health care law that Republicans loathe.

Romney has repeatedly said he didn’t intend for the federal government to copy Massachusetts.
“It was in your book that it should be for everybody,” said Santorum. “You took it out of your book.”
It was hard to hear Romney or Santorum as they talked simultaneously. “Rick, you had your chance. Let me speak,” Romney finally insisted, and reiterated his position.

The hardcover edition of Romney’s book, “No Apology,” said in March 2010 of the Massachusetts health care plan, “We can accomplish the same thing for everyone in the country, and it can be done without letting government take over health care.”

Three weeks later, the federal health care law was enacted, and Romney eliminated the clause about accomplishing the same for everyone in his paperback, published in February 2011.

Romney’s campaign explained the change came because the Obama plan was now law, requiring him to reword his writing.

Also participating at Tuesday’s debate was former House Speaker Newt Gingrich and Minnesota Rep. Michele Bachmann.

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