Boosted by his newly minted front-runner status, Republican presidential candidate Herman Cain bounced into Tuesday's GOP debate in Las Vegas as the latest possible conservative foil to Mitt Romney.

So ... naturally Cain and his "9-9-9" tax plan became the immediate focus of attacks from the group of Republicans hoping to knock him off stride.

9-9-9, Cain says, is the first step to creating a national flat or "fair" tax. It would replace the current complicated tax system with 9 percent personal income tax, a 9 percent national sales tax and a 9 percent tax on businesses. Unlike the current system, Cain's plan includes relatively few opportunities for people or businesses to claim deductions or write off expenses. The personal income tax, for example, would include only two potential exemptions -- people could write off donations to charity and tax filers would get a break for living in impoverished inner cities. Cain's national sales tax would be on top of state and local sales taxes. (You can read a more detailed background of the plan here.)

More people have started to criticize Cain's plan, saying it's a regressive series of taxes that will force poorer and middle-class Americans to pay more in federal taxes.

After an initial attack from U.S. Rep. Michele Bachmann Tuesday, Cain responded to CNN moderator Anderson Cooper by saying that 9-9-9 "does not raise taxes on those that are making the least." That, he said, is "simply not true."

However, a PolitiFact analysis of Cain's plan -- relying on three different tax accountants -- found a similar statement Mostly False.

The debate then turned to health care -- and Romney's role in pushing changes to Massachusetts' health care laws while he served as governor. Romney tried to deflect criticism by noting that state residents support the change by a 3 to 1 margin. That claim rates True.

Romney also pointed out that former U.S. House Speaker Newt Gingrich supported an individual mandate, the now controversial part of President Barack Obama's health care law. Republicans, it turns out, actually proposed an individual mandate back in 1993.

As the debate pivoted to illegal immigration, Texas Gov. Rick Perry accused Romney of hiring illegal immigrants, a claim that Romney strongly denied. "You had illegals working on your property," Perry said. Romney said he hasn't employed an illegal alien, a claim we rated Mostly False.

Bachmann made a series of claims about the cost of illegal immigration. While her numbers are new to us, including a figure that every household pays $1,000 to support illegal immigrants, our state partners have looked into the cost of illegal immigration before. Often, the claims are overstated (Florida). (Ohio.) (Georgia.)

The debate then turned to a concern of Nevadans, a plan to store nuclear waste at site at Yucca Mountain. U.S. Rep. Ron Paul and Romney said they opposed the plan, saying the federal government shouldn't tell Nevada that it has to store nuclear waste from across the country. You can read a good background on the plan, told through a claim from Senate Minority Leader Harry Reid of Nevada.

From there, talk turned quickly to the Troubled Asset Relief Program, better known as TARP, which passed in 2008. Former U.S. Sen. Rick Santorum said the plan was a mistake and criticized Perry for supporting it. Perry said Santorum had his facts wrong. Our friends looked at a similar statement from Perry about his non-support for TARP and ruled it Half True.

When an audience member why the United States continues to give foreign aid, Perry said the country needed to have a "real debate" about cutting foreign aid spending. As PolitiFact previously has noted, foreign aid currently makes up 1 percent of the federal budget, with Israel receiving a significant chunk of the support in military and economic aid.

Romney, Perry and Santorum later played a game of who use to be more liberal (though no one was accusing Santorum of being liberal). Romney pointed out that Perry chaired Al Gore's campaign for president. We rated a similar claim from Bachmann Half True. And Santorum said Romney ran for office in 1994 to the left of former U.S. Sen. Ted Kennedy. Though Santorum's claim lacks some of the nuance, the Truth-O-Meter actually heard a similar statement back in 2007 from former New York City Mayor Rudy Giuliani.

"He's (Romney) the one who said that he would be to the left of Teddy Kennedy on gay rights," Giuliani said back in 2007. That specific claim rated Mostly True.

(Keep checking back to PolitiFact.com for fact-checks on new statements from Tuesday's debate.)