The future of Medicare, the federal health program for the elderly and disabled, has become a flash point in the campaign since Mitt Romney’s selection last month of Rep. Paul Ryan (Wis.), chairman of the House Budget Committee, as his running mate. (Christian Murdock/AP)

Voters in three critical swing states broadly oppose the far-reaching changes to Medicare ­associated with the Republican presidential ticket and, by big margins, prefer President Obama to handle the issue, according to new state polls by The Washington Post and the Kaiser Family Foundation.

For seniors in Florida, Ohio and Virginia, Medicare rivals the economy as a top voting issue. And by majorities topping 70 percent, seniors say they prefer to keep Medicare as a program with guaranteed benefits, rather than moving to a system in which the government gives recipients fixed payments to buy coverage from private insurers or traditional Medicare, as Romney advocates.

Among all voters, the desire to keep the system as it is peaks at 65 percent in Florida, where more than one in five Americans who voted in 2008 were age 65 and older.

Generally, the more voters focus on Medicare, the more likely they are to support Obama’s bid for reelection.

The future of Medicare, the federal health program for the elderly and disabled, has become a flash point in the campaign since Romney’s selection last month of Rep. Paul Ryan (Wis.), chairman of the House Budget Committee, as his running mate. The choice of Ryan — who wrote a proposal that would move Medicare toward vouchers as part of an overall attempt to curb the deficit — is considered a bold and politically risky move, given Medicare’s popularity.

Now, the challenges for Romney in the aftermath of the Ryan selection are becoming clear.

Although Obama faces his own problems among voters over health care, the fresh attention to Medicare appears to be blunting the negative fallout from his 2010 health-care reform law.

Romney has revived a Republican line of attack from the midterm elections that year, charging that Obama “raided” Medicare “to pay for Obamacare.” The criticism refers to $716 billion in cuts to Medicare in the health-care law — cuts that Ryan previously supported but has since said he would undo.

The law, which the Supreme Court largely upheld, remains controversial and is, according to an analysis of these new poll results, a drag on Obama’s reelection prospects. In Florida and Ohio, more voters have “strongly unfavorable” than “strongly favorable” impressions of the legislation.

But voter distaste for a Ryan-like plan may insulate Obama from the political fallout. It appears that Medicare may have become a winning issue — for Obama.

In Virginia, Cheryl Schaffer, 64, said she will vote for Obama in part because of his differences with Romney on Medicare.

“I’m hoping to have Medicare in six months,” said Schaffer, a Richmond retiree. “I don’t like what Romney is going to do to it.”

Romney campaign spokeswoman Andrea Saul said the poll findings were “irrelevant” because the question on the type of Medicare overhaul that Romney advocates did not accurately describe the plan. In an e-mail, she said that respondents were not told that Romney has promised not to change Medicare for Americans older than 55.

She said it also was misleading to present voters with the alternative of leaving Medicare as is, “considering the program will go bankrupt.”

“Words matter,” Saul said. “None of those descriptors were in the question, and that wildly changed the understanding of Governor Romney’s plan.”

The poll question did not mention Romney or Ryan by name.

Adam Fletcher, a spokesman for the Obama campaign, said, “Seniors recognize the stark choice they face on Medicare in this election because it couldn’t be clearer.”

“The unpopularity of the Romney-Ryan Medicare voucher plan is an opportunity for the president to close the gap among seniors as well as other demographics,” he said.

Medicare covers about 49 million seniors and disabled people and is an open-ended entitlement — it pays for all covered benefits. Its $549 billion in annual expenditures comes from taxpayer money and premiums paid by beneficiaries.

Although seniors nationwide dislike the idea of moving away from the current system, their opposition is even more pronounced in Florida, Ohio and Virginia, where both candidates have spent weeks saturating the airwaves with Medicare attack ads.

Obama hammers the Ryan plan continually, telling supporters at a campaign event in Milwaukee last Saturday that Romney and Ryan would “turn Medicare into a voucher program in order to pay for tax cuts for the very wealthy.”

Looking across the three states, voters age 50 and older tilt toward Obama on Medicare and split on which candidate will receive their vote, with 50 percent siding with the president and 45 percent with Romney.

This spells trouble for Romney, said Robert Blendon, a professor at Harvard University who monitors public views on health-care issues.

“For Governor Romney to be president, he has to win a huge majority of people over age 50. All President Obama has to do is to split that age group. So what really matters here is that the Medicare issue corresponds to the age group that is most critical to determining whether Romney will be president,” Blendon said.

The dynamic has contributed to Obama’s slim edge in Florida, where older voters make up a larger share of the electorate than in any other state. In Ohio and Virginia, he holds clear leads.

Underlying support for not changing Medicare is the widespread belief that the system is functioning smoothly. In Florida, 70 percent of all voters say the system is working well — rising to 91 percent of the state’s seniors — and positive assessments of Medicare are nearly as high in the other states.

Asked whom they trust to deal with the Medicare program, Ohio voters favor Obama over Romney by a margin of 19 percentage points. The president has a 15-point advantage on the issue in Florida and a 13-point lead on it in Virginia. In a separate national poll from the Kaiser Family ­Foundation, released Thursday, Obama’s 17-point lead over Romney on Medicare is larger than it has been across public polls all year. Seniors are more split on the matter. In 2008, Obama lost seniors by eight percentage points.

The importance of Medicare as an issue also boosts Obama more directly: In the three Post-Kaiser state polls, voters who call Medicare an “extremely important” voting issue side with him over his challenger, 59 percent to 36 percent, while those who consider it less than very important tilt toward Romney, 54 percent to 36 percent. Even among political independents, Obama support is higher among those who put a higher priority on the issue than among those less apt to focus on it.

There is also a widely held public perception that changes are needed to keep Medicare sustainable for future generations. The problem for Republicans is that swelling budget deficits are not a sufficient motivator for voters. Across the three states, about three-quarters of voters say that Medicare cuts are not essential to deficit reduction.

Felicia Sonmez, Ben Pershing and Scott Clement contributed to this report.