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.

Perry, whose poll numbers fell after he stumbled in debates 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.

Cain charged that his rivals were confusing "apples and oranges" by talking about adding the national sales tax to local sales taxes because people in those states would pay the local tax regardless.

"I'm going to get a bushel basket that has both apples and oranges because I'm going to have to pay both taxes," shot back Romney.

"It's regressive," added Rep. Ron Paul of Texas, noting that a sales tax hits lower- income families proportionately more than higher incomes because they have to spend far more of their income to live.

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.

Romney for several years used a lawn service at his home that employed undocumented aliens.

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 former Sen. Rick Santorum of Pennsylvania. "You took it out of your book."

Romney's hardcover 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.

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

Also participating in the debate were former House Speaker Newt Gingrich and Minnesota Rep. Michele Bachmann.

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