With President Obama campaigning aggressively on the message that Republican Mitt Romney would raise taxes on the middle class, conservatives stepped up their assault Tuesday on the study that forms the basis of Obama’s allegations.

Alex Brill, a research fellow at the American Enterprise Institute who served as a consultant to the president’s bipartisan fiscal commission, argues in a new analysis that the August study by the nonpartisan Tax Policy Center erroneously concludes that Romney would have to raise taxes on middle-class households by at least $86 billion a year to pay for his proposal to cut tax rates across the board by 20 percent.

Using his analysis, Brill outlines his reasons for why that $86 billion in tax hikes would not come to pass under Romney’s plan.

For one, he say, the TPC researchers failed to factor in the possibility that Romney could eliminate additional tax breaks that primarily benefit upper-income taxpayers, such as the tax-free treatment of interest on state and local bonds and the tax-free build-up of value in life insurance policies. Taxing that income, Brill writes, would raise about $45 billion a year from wealthy households, reducing the potential tax burden on middle-class households to $41 billion a year.

Romney has not yet given the details of the tax breaks he would eliminate as part of his reform plan.

In its study, the TPC did factor in new taxes on the wealthy that are included in Obama’s health-care initiative. Romney has proposed repealing those taxes — including a new 3.8 percent levy on investment income. But, Brill notes, the candidate “has not suggested that the cost of repeal would be paid for by tax reform.” Instead, Romney wants to repeal the new health-care spending that prompted Congress to levy the tax in the first place.

And so, Brill writes, there’s another $29 billion that doesn’t have to come out of the hide of the middle class. “A $41 billion tax increase shrinks to $12 billion.”

Finally, Brill contends, the TPC’s economic model fails to account for the likelihood that tax reform that lowers rates and simplifies the rules would boost economic growth. “If the economy were to grow just 0.1 percentage point faster per year as a result of the reform,” he writes, “the additional revenue . . . would be approximately $13 billion. The result: A $12 billion tax increase on the middle class actually becomes a tax cut.”

Brill’s analysis is the latest in a flurry of conservative critiques of the TPC study, which Obama added to his stump speech upon its release Aug. 1. The Obama campaign is also using the study to hammer Romney in TV ads.

On Tuesday, William Gale, co-director of the TPC and one of the study’s authors, defended the original report, saying it accurately described the trade-offs that would be required to achieve each of Romney’s five goals for tax reform: lowering marginal rates, repealing the alternative minimum tax, preserving tax breaks for saving and investment, maintaining the current distribution of the tax burden between rich and poor, and maintaining the level of tax collections so as not to increase the budget deficit.

“None of the ‘critics’ are showing that what we did was wrong or invalid,” Gale said in an e-mail. “Instead, they are showing ways of getting out of the five-way Gordian knot, and all of those ways involve violating one or more of the five items that led to the knot in the first place.” Taxing interest on state and local bonds or on the value in life insurance policies, for example, would violate Romney’s preference for preserving low taxes on savings and investment.

“So we are saying, ‘It is impossible to do these five things without raising taxes on households with income below $200,000.’ And they are saying, basically, ‘It is possible to do up to four of the things without raising taxes on households with less than $200,000,’” Gale said. “Everyone — including us — agrees that if you give up on some of the goals, give up on some of the proposed tax cuts, or [protect] a [less affluent] income group (under $100,000 for example), the plan can be financed without raising taxes on households with income below $200,000. We basically said that in the original paper.”

As the debate over the TPC study rages, other conservatives are looking for flaws in Obama’s tax plans. In a short paper published Tuesday, Douglas Holtz-Eakin, president of the American Action Forum, argues that Obama, too, would have to raise taxes on the middle class, to cover the cost of projected spending in his latest budget request and meet his goal of producing a balanced budget outside of interest payments.

Holtz-Eakin, a former director of the nonpartisan Congressional Budget Office, contends that the gap between Obama’s spending request and projected revenues, excluding interest on the debt, amounts to about $5 trillion through 2022. Even if half of that deficit were wiped out through lower spending, Holtz-Eakin argues, raising the rest of the money entirely by taxing those earning more than $500,000 a year would require increasing their federal tax rate to a prohibitive 63 percent.

“As a bottom line, the lesson is clear,” Holtz-Eakin writes. “It will not be possible [to protect] the middle class in the absence of spending reforms.”