The figures echo estimates by private forecasters and by the Congressional Budget Office.
According to the report, a married couple earning between $50,000 and $85,000 with two children would see a $2,200 increase in their taxes.
Congressional Republicans, led by Boehner, have said they are open to including discussions about additional revenue but have balked at any plan that raises tax rates on the wealthy. They argue that the higher rates would also hit some small businesses, stifling economic growth.
Instead, they have advocated changes in the tax code that would eliminate tax breaks and loopholes that primarily benefit the wealthy. Several key Republican lawmakers have also said they would not be bound by a no-tax-increase pledge that they have adhered to in the past.
Tennessee GOP Sen. Bob Corker is circulating a bill claiming $4.5 trillion in deficit savings over the coming decade, including $749 billion in higher tax revenue by capping itemized deductions at $50,000, a proposal that hits wealthier taxpayers the hardest.
Corker's plan — shared with the White House and congressional leaders — contains a roster of other budget proposals, including a less generous inflation adjustment for Social Security, and a gradual increase in Social Security eligibility to 68, and 67 for Medicare. Upper income earners also would pay more for Medicare.
But Carney said the tax revenue sought by Obama can't be achieved by simply restricting tax deductions
"Math tells us that you can't get the kind of balanced approach that you need without having rates be part of the equation," he said. "We haven't seen a proposal that achieves that, a realistic proposal that achieves that."
Associated Press writer Andrew Taylor contributed to this report.
Copyright 2012 The Associated Press. All rights reserved. This material may not be published, broadcast, rewritten or redistributed.