The near-weekly ritual of Republican presidential debates took a raucous turn Tuesday night as the unsettled field of candidates ganged up on one another in a series of attacks more intense and personal than any in their previous appearances together.

The first to feel the assault was the front-runner of the moment, Herman Cain, who is struggling to prove that he is a serious contender and not merely another evanescent phenom of this election season. He was thrown on the defense by new criticism of his signature “9-9-9” tax overhaul plan, which an independent analysis released shortly before the debate indicated would be a boon to the wealthy and put a significantly heavier burden on lower- and middle-income Americans.

But the other leading contenders each got their turn at the bottom of the pile. Previously unflappable former Massachusetts governor Mitt Romney appeared knocked off stride at times — particularly when Texas Gov. Rick Perry mentioned a 2007 episode in which Romney had hired a lawn company that employed illegal immigrants.

Perry noted that Romney himself has said “there was a magnet of people that will hire illegals,”adding: “And you are number one on that list, sir.”

At one point, a red-faced Romney shouted at Perry: “Are you just going to keep talking, or are you going to let me finish what I have to say?”

Indeed, it was a far feistier Perry who showed up for this debate, though he, too, found himself a target of the others several times, including in a testy exchange with former senator Rick Santorum (Pa.), who claimed that Perry had supported the 2008 government bailout of Wall Street.

“He sent a letter the day of the vote on the floor of the House saying, ‘Pass the economic plan,’ ” Santorum said, with Perry’s protest, “Wrong,” audible in the background. Perry said he was only urging Congress “to act.”

At one point near the end of the two-hour forum, former House speaker Newt Gingrich (Ga.) pleaded: “Maximizing the bickering is not the best road to the White House.”

The vitriol onstage was the product of the far larger dynamic in the GOP race, at a moment when the first early-voting contest, in Iowa, is less than three months away. The normally orderly process by which Republicans select a presidential contender has this year turned into a frenzied and fickle courtship that has seen opinion polls swinging from one infatuation to the next.

The leading candidates arrived at the forum with very different goals. Romney was hoping for another sure-footed performance in hopes of tamping down persistent doubts within the party that have prevented him from turning his establishment edge into a sheen of inevitability.

Perry, whom Romney’s advisers still consider his most formidable competitor, was seeking to regain the stature he had briefly as a top-tier candidate. That stature has suffered after a series of mediocre debate performances.

Rep. Michele Bachmann (Minn.), who also had a moment in the political sun before fading into the shadows after Perry entered the race, was also seeking to reemerge — although the fact that she was largely ignored by her aggressive rivals suggests they no longer consider her a threat.

Rounding out the group participating in the debate, which was sponsored by CNN and held at the Venetian hotel’s convention center, was Rep. Ron Paul (Tex.), who assailed the others for resisting cuts in defense spending, saying: “We want to spend more and more, and you can’t cut a penny? I mean, this is why we’re at an impasse. I want to hear somebody up here willing to cut something. Something real.”

Missing from the stage was former Utah governor Jon Huntsman Jr., who announced last week that he would boycott to register his protest to Nevada’s decision to move its caucuses to Jan. 14 — a move that violates Republican Party rules.

Of all the candidates to emerge from the pack in this volatile election cycle, Cain has been the most unlikely. His precarious position at the top of the field was made all the more so by a new study issued Tuesday by the nonpartisan Tax Policy Center on his 9-9-9 plan.

He has said that the plan would reduce taxes for most Americans, but the center said otherwise.

According to the analysis, Cain’s proposal would lower taxes for 95 percent of the nation’s millionaires an average of $487,000. The vast majority of taxpayers earning less than $100,000 would bear a tax increase.

Asked about the review of his plan — which would replace the current tax system with a 9 percent levy on individual income, corporate earnings and purchases — Cain dismissed it as a “knee-jerk reaction” that was refuted by his campaign’s calculations.

“The reason that my plan — the reason that our plan is being attacked so much is because lobbyists, accountants, politicians, they don’t want to throw out the current tax code and put in something that’s simple and fair,” Cain said.

But his rivals weren’t buying it.

“You don’t need to have a big analysis to figure this thing out,” Perry said. “Go to New Hampshire, where they don’t have a sales tax and you’re fixing to give them one.”

The debate came at a time when the party is trying to sort out its own identity amid the tension between its establishment wing and the insurgent forces represented by the tea party movement. Romney has been unable to consolidate the two, in part because of a relatively moderate history that includes enacting a health-care system in Massachusetts that strongly resembles Obama’s new national law.

“Your plan was the basis for Obamacare,” Santorum told Romney.

The question of whether Romney’s plan was a model for Obama’s health-care overhaul quickly deteriorated into a testy exchange over the origin of the landmark legislation.

It started when Gingrich declared that the Massachusetts plan called for far more government involvement in the provision of health care than Romney had claimed. But Romney countered that Gingrich himself, along with the conservative Heritage Foundation, had been among those who supported the idea of an individual mandate before Romney pushed it in his state.

“That is not true,” Gingrich interrupted — only to acknowledge, a moment later, that he had, in fact, supported the individual mandate.

Romney has sought throughout the campaign to bolster his bona fides with the right. However, Perry was clearly aiming to stir those doubts about his rival as he introduced himself to the debate audience as “an authentic conservative, not a conservative of convenience.”

Perry was asked if he would repudiate the remarks of the Rev. Robert Jeffress, who called Romney’s religion, Mormonism, a cult after introducing Perry at the Values Voter Summit in Washington earlier this month. Perry said he disagreed with Jeffress’s views, but Romney added that it was something else Jeffress had said that was most disturbing to him — that to choose a president, voters must first “inspect his religion.”

“It was that principle, Governor, that I wanted you to be able to say, ‘No, no, that’s wrong, Reverend Jeffress,’ ” Romney said.

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