WASHINGTON (AP) — A new Republican budget would repeal President Barack Obama's health care overhaul but put future retirees in a version of Medicare that strangely resembles one of the key cogs in that same plan.

Sound contradictory?

Rep. Paul Ryan, R-Wis., the top GOP budget writer, borrowed the idea of insurance exchanges, a big pooled marketplace, from the health care law enacted in Massachusetts when GOP presidential candidate Mitt Romney was governor. Ryan wants to set one up for Medicare.

Obama borrowed the same idea to make exchanges available to uninsured working families through his law.

Experts who see some agreement rather than irreconcilable differences are scratching their heads and wondering if politicians of both parties may have more in common than they care to admit to voters in the heat of an election year.

"It's almost as if the roles of the players are being reversed," said Sen. Ron Wyden, D-Ore. "It is almost ideologically incoherent." A centrist, Wyden is co-author of a version of the Ryan Medicare plan and also voted for Obama's health care law. He does not support the spending cuts in Ryan's latest plan.

"There does seem to be an odd inconsistency on both sides," said economist Gail Wilensky, who ran Medicare for President George H.W. Bush and advises Republicans.

Ryan's new budget would begin a gradual shift, reshaping Medicare for retirees, starting with the tail end of the baby-boom generation. The basic government program would remain in place for current beneficiaries and anyone now 55 or older.

But future retirees now 54 or younger would get a payment from the government — called premium support by Republicans and a voucher by Democrats — to pick a health insurance plan through a new Medicare exchange. Private insurance plans would compete directly with a new government option modeled on the traditional program in the Medicare marketplace.

It's close to the idea that Obama originally tried to get through Congress back in 2009. Early versions of the president's overhaul featured a competition between private insurance and a government plan.

"On the one hand, (Ryan's) proposal repeals exchanges created under the health reform law to provide coverage for the uninsured, while on the other, sets up new insurance exchanges for already insured seniors," said Tricia Neuman, top Medicare policy expert for the nonpartisan Kaiser Family Foundation, an information clearinghouse on the health care system.

To be sure, there are many major differences between the latest GOP plan and what the president and the Democrats support.

Chiefly, the GOP plan envisions holding the cost growth of Medicare well below long-range forecasts for the next 40 years. On top of that, it calls for ending the federal entitlement to health care for the poor, turning Medicaid over to the states. Spending on that program would plunge as a share of the overall economy. Many of Medicaid's costliest cases are low-income elderly patients with serious disabilities.

"The bigger issue here is whether the constraints on government spending will result in seniors paying more for the same set of benefits they get today and what all of these changes, taken together, will mean for their costs and care," Neuman added.

Republicans attacked Obama's health care law for cutting Medicare by $500 billion, warning it could lead to hospitals going out of business, reducing access for seniors and stifling promising new medical technologies. On Tuesday, the nonpartisan Congressional Budget Office said the new GOP plan runs the same risks — only worse.

"At least some of those effects would of necessity be a great deal stronger (under the GOP plan) because spending would be so much lower," the CBO said in an early analysis.

The proposed Medicaid cuts are too deep even for some Republicans.

"I am not sure I am comfortable with the level of reductions implied here," said Wilensky, who also oversaw Medicaid when she was in government. "The numbers, I think, are pretty drastic."

Medicaid is now a federal-state partnership through which Washington provides most of the funding and writes most of the rules. Wilensky questions turning it over to the states.

A grand bargain on deficits and the budget eluded Obama and House GOP leaders last year. With the election approaching, it's even less likely this year.

But if Obama is re-elected and his health care law is upheld by the Supreme Court, Wyden sees Medicare exchanges and a premium support system as the basis for a deal to reduce health care costs. He said Democrats would be hard pressed to argue against the idea if it is working for people under 65 as a result of the health care overhaul.