Stumping for votes in the pivotal battleground of Ohio, President Barack Obama hammered Mitt Romney's tax plan on Wednesday, highlighting a new study that said the Republican challenger's blueprint could leave poor and middle-class Americans paying more to the IRS to offset tax cuts for the wealthiest.

"If Gov. Romney wants to keep his word and pay for this plan, then he'd have to cut tax breaks that middle-class families depend on to pay for your home, the home mortgage deduction; to pay for your health care, the health care deduction; (or) to send your kids to college," the president said.

"And here's the thing: He's not asking you to contribute more to pay down the deficit, he's not asking you to pay more to invest in our children's education, or rebuild our roads or put more folks back to work," Obama said in Mansfield, Ohio. "He's asking you to pay more so that people like him can get a big tax cut."

The Romney campaign charged that "glaring gaps" in the study invalidated its analysis and accused Obama of trying to distract voters from the sputtering economy.

Both sides were sparring over a new independent study by the Brookings Institution think tank and the Tax Policy Center that found Romney's tax plan would leave millionaires paying less in taxes and the poor and middle class paying more. (Romney aides noted that one of the study's authors is a former member of Obama's Council of Economic Advisers. But another author, William Gale, served on President George H.W. Bush's Council of Economic Advisers. And Democrats noted that the Romney campaign had described the Tax Policy Center as providing "Objective, Third-Party Analysis" when using its analysis of former Romney rival Rick Perry's plan back in November.)

The former Massachusetts governor has called for extending the tax cuts first championed by President George W. Bush in 2001 and 2003 and extended by Obama in late 2010. His approach would also reduce rates an additional 20 percent, and abolish taxes on investment for Americans making under $200,000. But his blueprint is notably vague on how it would avoid expanding the deficit.

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The study found that taxes for households making less than $200,000 would go up $500 a year on average, while taxes for households making more than $200,000 would drop. Tax savings would be $1,800 for households making $200,000-$500,000, $17,000 for those making $500,000 to $1 million, and $87,000 for those making $1 million or more.

"It is not mathematically possible to design a revenue-neutral plan that preserves current incentives for savings and investment and that does not result in a net tax cut for high- income taxpayers and a net tax increase for lower- and/or middle-income taxpayers under the assumptions we have described above," the study's authors wrote.

Romney's proposals to cut income and estate taxes would shrink federal revenues by $360 billion in 2015. And the Republican's pledge not to widen the deficit "would require deep reductions in many popular tax benefits ranging from the mortgage interest deduction, the exclusion for employer-provided health insurance, the deduction for charitable contributions, and benefits for low- and middle-income families and children like the EITC (Earned Income Tax Credit) and child tax credit."

Republicans often say that more money in the pockets of higher-income Americans means more investment, which means more jobs and therefore more income—suggesting that a tax cut could in theory partly pay for itself.

But the study crunched the numbers and reported that "even generous assumptions regarding the ability of tax cuts to partially pay for themselves does not change the basic qualitative results."

Romney policy director Lanhee Chen assailed what he called "glaring gaps" in the study—homing in on the authors' decision not to factor in the Republican's proposal to lower corporate tax rates to levels comparable to those in other countries, as well as their decision to exclude potential spending cuts.

"Unfortunately, President Obama and his allies are simply trying to distract attention from his failed record on the economy," Chen said in a statement. "The American people know better than to fall for these distractions."

(The study said that the precise impact of spending cuts would depend on which programs felt the ax. "It is likely, however, that cutting spending would make the plan even more regressive because government spending tends to benefit low- and middle-income households more than tax preferences do," it said.)

Obama's trip to Ohio also highlighted a local controversy. Buckeye State media reported that Air Force One landed at an air base set to be shuttered under the president's proposed cuts in defense spending.

UPDATE 5:24 p.m.: This post was updated to include Romney policy director Lanhee Chen's response to the study.