Newt Gingrich, Mitt Romney get nasty. Will it backfire? (VIDEO)

The kid gloves are off.

Both Mitt Romney and Newt Gingrich – the two GOP front-runners – are targeting each other in increasingly nasty ways (despite Mr. Gingrich's promises to stay positive).

Most recently? Mr. Romney, the former Massachusetts governor, told Fox News on Monday morning that Gingrich should pay back the $1.6 million he took in fees for advising Freddie Mac, an agency that buys home mortgages from commercial lenders and was kept afloat by the government during the financial crisis.

"One of the things that I think people recognize in Washington is that people go there to serve the people and then they stay there to serve themselves," Romney told Fox.

He also mocked Gingrich's earlier defense that he never lobbied for Freddie Mac but rather served as a historian. "That would make him the highest-paid historian in history," said Romney.

Gingrich immediately shot back. "If Governor Romney would like to give back all the money he's earned from bankrupting companies and laying off employees over his years at Bain [Capital], then I would be glad to then listen to him," the former House speaker told reporters Monday. “I would bet you $10, not $10,000, that he won’t take the offer.”

That last line is in reference to Romney's gaffe over the weekend in which he offered to bet Texas Gov. Rick Perry $10,000 that Perry's statements about Romney's book are wrong. (Governor Perry claims that in the first edition of the book, Romney wanted to impose an individual health-insurance mandate at the federal level.)

Romney was instantly attacked by both Democrats and Republicans for the size of the bet, saying it showed he was out of touch with average Americans.

At the same time, Romney – who until recently focused more of his energies on Perry as his strongest opponent – has launched a new anti-Gingrich website called UnreliableLeader.com.

The nastiness could backfire, since voters tend to react negatively to candidates whom they see as too negative. And in Iowa – which holds the first event of the primary calendar, with caucuses in about three weeks – voters are famous for disliking campaign nastiness. One Washington Post columnist goes so far as to suggest that this may have happened to the Democrats in 2004, with Howard Dean and Dick Gephardt taking each other on with such ferocity that it destroyed them both, allowing John Kerry to emerge as the victor. The columnist, Jonathan Bernstein, wonders whether the ultimate beneficiary of the Gingrich and Romney feud might be Perry or Rick Santorum.

But given the polls, it's hard to see that happening. It's true, however, that Romney's 18 percent average in Iowa is hardly strong: Ron Paul – who has also run negative ads against Gingrich – trails him by just two points, and Perry by nine points. Even Gingrich's standing (about 30 percent) is tenuous, especially since his rise in the polls is so recent.

Gingrich, at least, still seems to consider himself above the fray – despite his snipes at Romney. On Monday, Gingrich told reporters in New Hampshire he has faith that the "American people figure out that running all those negative ads is a sign of somebody that's desperate."

"The contest between here and winning the nomination is going to be the power of positive ideas versus the power of negative advertising," he added. "I'm the front-runner, so everybody's going to pile on, and they're going to try to knock me down."