That is because multimillionaires are less dependent overall on deductions to shield their income; instead, they rely on things like low capital gains rates on investments and low dividend rates.

Limiting deductions for the one-third of Americans who file itemized returns would increase taxes most heavily for the wealthy, but in many cases it will reach further down the food chain than Obama’s proposed increase in the top tax rates — which would be strictly limited to upper brackets.

“By limiting itemized deductions, you will hit the rich harder than the middle class. They are more likely to itemize. And when they itemize, they itemize a lot more stuff. And their tax savings is bigger. At a 35 percent marginal rate, every dollar deduction saves you 35 cents,’’ said Roberton Williams, a senior fellow at the Tax Policy Center, a nonpartisan research group in Washington.

“But the problem with doing it with itemized deductions is it does hit that middle-income group more than if you just do it with rates,’’ he said. “So it’s not a matter of not being progressive. It’s a question of not being progressive enough.’’

Opinion polls indicate that Obama’s approach to taxes is more popular than Boehner’s. A Washington Post/ABC News poll released last week said 60 percent support raising taxes on the wealthy. When it comes to limiting deductions, 49 percent oppose the concept, while 44 support it.

Such poll numbers have given Democrats confidence that they have Republicans on the defensive as the White House and congressional leaders negotiate ways to avoid the fiscal cliff, that combination of across-the-board tax increases and automatic spending cuts scheduled to take effect on Jan. 1. Economists warn that the country would slip into recession sometime next year if the tax hikes and spending cuts draw too much money out of the economy.

If no deal is in sight at the end of the month, some Democrats are prepared to allow the automatic tax hikes to occur, then put Republicans even further on the defensive by immediately pushing a bill in early January to restore Bush-era tax cuts only for the 98 percent who make less than $250,000.

Williams, of the Tax Policy Center, called those lawmakers “cliff divers.”

Their strategy carries risks, he said, because their ability to push through tax cuts and stave off automatic budget reductions after the new year is not guaranteed.