DENVER -- A comment by Republican presidential nominee Mitt Romney earlier this week regarding how he would overhaul the U.S. tax code set off a back-and-forth between the Romney and Obama campaigns on Wednesday.

The Obama campaign seized on Romney's comments in an interview with a local TV station in Colorado Monday night, saying that his mention of a possible $17,000 cap on itemized deductions would mean higher taxes for "many families."

The campaign used the example of a family of four making $125,000 a year, and another of a family of three with an annual income of $85,000. Both, the Obama campaign said, would claim more than $17,000 a year in tax deductions, meaning that under Romney's idea of a cap they would pay more than they do now.

But a Romney campaign adviser not authorized to speak publicly said that the biggest number used by the Obama campaign to come up with its result was one not included under a cap system: the tax exclusion for employer-provided health insurance. This was a $16,000-a-year value under the Obama campaign example, but without that number, in its scenarios the two families would get a tax cut, instead of paying more, according to the Romney advisor.

An Obama campaign adviser, who spoke on the condition he not be identified, said that "even if health is not included, it's very easy to get to the same math starting with the mortgage interest deduction."

"It's not uncommon for people to spend 20 to 25 percent of their income on home mortgage," he said. "So if you are making $80,000 a year, you could easily be spending more than $17,000 on mortgage insurance when you're a new homeowner."

The Obama adviser said that the campaign had included the health care exclusion in its scenario because "the way the governor talked about it on Monday he listed three things and one of them was health insurance."

The Romney campaign official said that there are miscellaneous health care deductions that could come under such a cap, but that the exclusion for employer-provided health insurance is different than a deduction.

Romney's comments Monday were not meant to be a rollout of a new policy, but rather a reference to one of a few options, said Romney's top policy adviser, Lanhee Chen.

"Governor Romney's tax reform plan will jumpstart economic growth, cut the tax burden on the middle-class, and lower tax rates across-the-board," Chen said in an e-mail. "He will pursue revenue and distributional-neutrality in reforming the tax code. There are a range of policy options, and Gov. Romney referenced one illustrative example, to achieve these goals."

Martin Feldstein, a Harvard University economist who advises Romney, has argued for a cap on deductions but on a percentage basis, not a hard-dollar amount.

The Obama adviser said that the comment "kind of has the ring of something that came up in debate prep and just kind of came out."

Romney's tax proposal so far has been to lower rates for all tax brackets by 20 percent, and to eliminate tax loopholes while achieving deficit neutrality. Obama's team has made it a centerpiece of its campaign to argue that Romney's plan will cut taxes for millionaires and billionaires, while forcing middle-income Americans to pay for it when the tax deductions that they most utilize are eliminated.

Roberton Williams of the Tax Policy Center told BusinessWeek that the idea of a cap on deductions "targeting high-income people ... would hit them pretty hard." TPC issued a paper in August that argued that Romney would raise taxes on middle-income Americans.

Romney's campaign has pushed back hard this week, pointing to a paper by a conservative think-tanker saying Romney's plan does not raise taxes on the middle class, and mentioning the idea of the cap.

The Wall Street Journal wrote on Wednesday that "in 2009, the average break for those who itemized was about $26,000, according to Internal Revenue Service data."

"Only households that earned less than $45,000 a year averaged less than $17,000 in deductions," the Journal wrote.

If those numbers are accurate, some middle-income earners under a $17,000 a year tax deduction cap would pay no more, some would get a tax break and others above that $45,000 a year mark might have to pay more.

UPDATE: 8:30 p.m. -- Obama campaign spokesman Adam Fetcher said in an e-mail that Romney had muddied the water about what his intentions are.

"Another day brings two more descriptions of Governor Romney's tax plan. Just today, his campaign told one news outlet that his $17,000 cap does not apply to tax benefits for employer health premiums, while telling another that he would create a separate cap on that same tax benefit and limit credits like those that help families pay for child care and college," Fetcher said, pointing to a BusinessWeek article. "Give him credit -- he is now admitting that middle-class tax increases on housing, health care and charitable deductions are on the table."

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