President Obama’s landmark health-care initiative, long touted as a means to control costs, will actually add more than $340 billion to the nation’s budget woes over the next decade, according to a new study by a Republican member of the board that oversees Medicare financing.

The study is set to be released Tuesday by Charles Blahous, a conservative policy analyst whom Obama approved in 2010 as the GOP trustee for Medicare and Social Security. His analysis challenges the conventional wisdom that the health-care law, which calls for an expensive expansion of coverage for the uninsured beginning in 2014, will nonetheless reduce deficits by raising taxes and cutting payments to Medicare providers.

The 2010 law does generate both savings and revenue. But much of that money will flow into the Medicare hospitalization trust fund — and, under law, the money must be used to pay years of additional benefits to those who are already insured. That means those savings would not be available to pay for expanding coverage for the uninsured.

“Does the health-care act worsen the deficit? The answer, I think, is clearly that it does,” Blahous, a senior research fellow at George Mason University’s Mercatus Center, said in an interview. “If one asserts that this law extends the solvency of Medicare, then one is affirming that this law adds to the deficit. Because the expansion of the Medicare trust fund and the creation of the new subsidies together create more spending than existed under prior law.”

Administration officials dismissed the study, arguing that it departs from bipartisan budget rules used to measure every major deficit-reduction effort for the past four decades — including the blueprint offered last month by House Budget Committee Chairman Paul Ryan (R-Wis.).

“Opponents of reform are using ‘new math’ while they attempt to refight the political battles of the past,” a White House budget official said, speaking on the condition of anonymity because the report was not publicly available. “The fact of the matter is, the Congressional Budget Office and independent experts concluded that the health-reform law will reduce the deficit. That was true the day the bill was signed into law, and it’s true today.”

Blahous acknowledged that his analysis departs from budget conventions, which, he said, make sense for the most part. He said that in this case, however, those rules do not fully illuminate the financial impact of the health-care law, since they permit what conservative critics have dubbed a “double counting” of proposed Medicare savings.

Medicare is financed in part through a trust fund that receives revenue from payroll taxes. Before Obama’s health-care act passed, the trust fund was projected to be drained by 2017 (later updated to 2016). Absent the health-care law, Blahous writes, Medicare would have been forced to enact a sharp reduction in benefit payments in the middle of this decade, or “other Medicare savings would have had to be found.”

Enter the health-care law, which provides about $575 billion in Medicare savings — enough to automatically extend the life of the trust fund through 2029, according to estimates at the time, and avoid a sharp cut in benefits.

But in cost estimates by the nonpartisan CBO, those savings also offset a dramatic expansion of Medicaid under the law, as well as new subsidies for uninsured people to purchase coverage.

CBO and Medicare actuaries acknowledge the double-counting issue. “In practice, the improved [trust fund] financing cannot be simultaneously used to finance other federal outlays (such as the coverage expansions) and to extend the trust fund, despite the appearance of this result from” traditional budget rules, Medicare actuary Rick Foster wrote last year.

And in 2010, the CBO wrote that, absent the Medicare savings, the law would increase deficits by $226 billion through 2019 — instead of decreasing them by the commonly cited $132 billion.

In arriving at his deficit figure of $340 billion, Blahous updates the numbers through 2021 and subtracts savings that would have come from another provision of the law: the CLASS Act, a long-term-care program that was supposed to have generated as much as $86 billion in new revenue through 2021. The administration acknowledged last year that the CLASS Act is unworkable and suspended efforts to implement it.

“This isn’t just a persnickety point about the intricacies of budget law,” Blahous said. “If Medicare were going insolvent in 2016, you’d better believe right now there would be more pressure on lawmakers to do something about it. . . . It’s essential that there be a full public understanding of the most economically significant federal law in years.”