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.”

For the first time in eight debates, the location itself was subject of some debate.

One candidate, former Utah Gov. Jon Huntsman, boycotted the debate Tuesday because Nevada has picked a date for its caucuses — Jan. 14 — that comes too close to the Jan. 10 date that New Hampshire wants.

Huntsman is eager to woo voters in New Hampshire, where the primary gets massive media coverage. He and others say they’ll boycott Nevada’s entire caucuses if it doesn’t change its date to accommodate New Hampshire.