The reason: Obama's cuts also extended the life of Medicare's giant trust fund, and by repealing them Romney would move the insolvency date of the program closer, toward the end of what would be his first term in office.
Instead of running out of money in 2024, Medicare says its trust fund for inpatient care would go broke in 2016 without the cuts. That could leave a President Romney little political breathing room to finalize his own Medicare plan.
The Romney campaign says there's no problem with the candidate's pledge.
"The idea that restoring funding to Medicare could somehow hasten its bankruptcy is on its face absurd," said spokeswoman Andrea Saul.
Campaign officials say arcane federal accounting rules create a false sense of security about Medicare. They allow savings like Obama's cuts to also count toward funding other programs or reducing the overall deficit.
"Gov. Romney's plan is to repeal Obamacare and replace it with patient-centered reforms that control cost throughout the health care system and extend the solvency of Medicare," Saul said. "He will then implement real entitlement reform that places Medicare on a sustainable long-term footing so that future generations of Americans will not have to worry whether the program will be there for them."
But Obama's cuts were not directly aimed at Medicare's 48 million beneficiaries; instead they affect hospitals, insurers, nursing homes, drug companies and other service providers. Simply undoing the cuts would restore higher payments to those service providers. And that would cause Medicare to spend money faster.
Romney's running mate, Wisconsin Rep. Paul Ryan, kept the Obama cuts in his budget, which envisions greater savings by shifting future retirees into private insurance plans with a fixed payment from the government to help cover their premiums.
"If you are going to restore (Obama's cuts), then what it's going to do is complicate the financial condition of Medicare," said former U.S. Comptroller General David Walker, a fiscal conservative who says government health care programs are too costly.
"It's going to affect your long-term plan to reform Medicare and reduce the deficit and mounting debt burdens," said Walker, now heading the Comeback America Initiative, which promotes deficit reduction.
"If you are going to put that back, then how are you going to pay for it?" he asked.
Romney would "have to find other ways to get the cost down in the future," said economist Marilyn Moon, a former trustee overseeing Social Security and Medicare finances.
"These (Obama cuts) were all on service providers," said Moon, now director of the health program at the nonpartisan American Institutes for Research. Romney "would have three options: either cut it out of providers in a different way, ask beneficiaries to pay higher premiums in various ways, or raise taxes in order to pay for it."
Romney made his promise to restore the cuts on Tuesday at a campaign stop in Beallsville, Ohio.
Obama "has taken $716 billion out of the Medicare trust fund," Romney told supporters. "He's raided that trust fund.
"And you know what he did with it? He used it to pay for Obamacare, a risky, unproven, federal takeover of health care," Romney continued. "And if I'm president of the United States, we're putting the $716 billion back."
That figure reflects the latest estimates of Obama's health care law by the Congressional Budget Office, covering a 10-year period from 2013-2022. It's a relatively modest share of total Medicare spending, currently about a $600 billion-a-year program.
"People need to look at what these spending reductions are before they conclude that they are really eager to undo them," said Paul Van de Water, a senior budget analyst with the liberal Center on Budget and Policy Priorities. "Why should Medicare beneficiaries want to pay more to providers to provide the same benefits?"
Despite its long-term financial problems, Medicare has been fairly stable since the passage of Obama's health care law. Premiums have remained about the same, reflecting a national slowdown in medical inflation. However, the brunt of the spending cuts has yet to be felt. Medicare's own economic forecasters have warned the cuts may prove politically unsustainable.
Romney has not spelled out full details of his Medicare plan. But if it is based upon Ryan's, the budget office says it would rein in Medicare spending more forcefully than Obama has.