New Jersey Gov. Chris Christie would like to raise the age to qualify for Medicare, part of a bold plan to reform entitlements that he released Tuesday morning.

The proposal was greeted with cheers from many conservatives, but there’s a twist. The main reason that slowly raising the retirement age from 65 to 69 is politically feasible is a law that many conservatives hate: Obamacare.

That’s because working-class Americans who lose health insurance at work when they retire at, say, age 65, would instead be eligible to receive modest subsidies on insurance exchanges set up by the Affordable Care Act. (Very low-income seniors could also sign up for Medicaid in some states or receive larger subsidies for coverage on the exchanges.)

“Obamacare soaks up the people who would otherwise be displaced by raising the eligibility age for Medicare,” said Avik Roy, a prominent Republican expert in health care policy who has argued that conservatives should use Obamacare to promote their own policies rather than repeal the law. “In the old days, if you raised the eligibility age for Medicare, then someone who is low-income at 65, but not eligible for Medicaid, are stuck in this gap, so what do you do?”

“But with [Obamacare], that safety net is there, so it’s much easier to raise the Medicare age,” added Roy.

But if retirees who, at 65, would have qualified for Medicare, which is relatively cheap, shift en masse to private insurance, which is relatively expensive, does Christie’s plan of raising the eligibility age actually save any money?

That answer has been hotly debated for years, since the cost of providing health care to 65-69 year-olds wouldn’t just disappear, it would shift to another part of the federal budget.

Some argue that it would save money, since the subsidies under the Affordable Care Act get smaller as seniors’ income rises, while Medicare serves seniors of all incomes the same.

“In general, raising the eligibility age for Medicare will save money for the federal government because seniors with relatively higher incomes wouldn’t be eligible for any other federal subsidies,” said Michael E. Chernew, a professor of health care policy at Harvard Medical School. “That’s the simple analysis.”

A 2011 Kaiser Family Foundation study estimated that raising the eligibility age for Medicare from 65 to 67 would save the federal government as much as $5.7 billion in the short term. But it could also cost 65- and 66-year-olds $3.7 billion in out-of-pocket expenses, and employers $4.5 billion in retiree health-care costs. (And that’s to say nothing of how the policy could negatively affect the cost of Medicaid and Medicare Part B premiums, according to the Kaiser study.)

Chernew added that raising the Medicare age comes with other, more complex ramifications, including the type and quality of care available, and whether such a policy would encourage more older Americans to remain in the workforce for longer. Another part of Christie’s plan directly incentivizes Americans to keep working past the age of 65 by eliminating the payroll tax for workers 62 and older.

But the broader question is whether conservatives want to make use of the Affordable Care Act to make their own changes to the health care system or whether they want to repeal the law and start from scratch.

Roy, who has advocated for “transcending Obamacare,” argues that that Christie’s policy proposal is a smart political play. “He’s staking out ground as a credible, bipartisan entitlement reformer,” he said.

Write to Haley Sweetland Edwards at haley.edwards@time.com.

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