The polls’ findings on Medicare underscore the risk Mr. Romney took when he chose Mr. Ryan to be his running mate. Mr. Ryan rose to prominence among conservatives who lauded his willingness to propose unpopular measures to balance the budget and cut the rising costs of Medicare — costs officials in both parties agree are on an unsustainable path. But while the polls found that Mr. Romney enjoyed a wide advantage in all three states on the question of who is better equipped to tackle the budget deficit, it found that he lagged on other questions voters feel strongly about — including who is better equipped to handle health care, Medicare and foreign policy. Some voters give them credit for campaigning on a politically contentious issue.

“It may be political suicide, but at least Romney and Ryan are willing to stand up and say we can’t keep shoveling money into this program and other programs like this,” said Michael Behnke, 59, an independent from Solon, Ohio.

When it comes to the running mates, Mr. Ryan comes out ahead with independents. On balance, they feel more favorable toward Mr. Ryan but have a more negative view of Vice President Joseph R. Biden Jr., who has drawn criticism in recent days for saying that Mr. Romney’s policies would unchain the financial sector and “put y’all back in chains.” But many voters in Florida and Ohio said they did not yet know enough about Mr. Ryan to form an opinion — and many in all three states said the choice of running mate would have no impact on their votes.

The polls were conducted by telephone (landline and cellphones) from Aug. 15 through Tuesday among 1,241 likely voters in Florida, 1,253 likely voters in Ohio and 1,190 likely voters in Wisconsin. All three are states Mr. Obama won, but where Republicans have since made gains in state and local elections.

Mr. Romney has taken pains to stress that his Medicare plan would not change the benefits for people 55 or over. But voters over 55 have strong feelings about it, including in Florida, the electoral-vote-rich state where Republicans will hold their convention next week.

Jim Ryan, 75, a retired executive from Bradenton, Fla., who is an independent, said it was an important issue because he and his wife were on Medicare.

“We’re enjoying the benefits now, and the Paul Ryan program of making it into a voucher system would change things,” he said. “I know it’s not intended to apply to people in our age group, but I’m concerned about the future. I think it’s a wonderful program, and I’ve got middle-aged children and I don’t want to see the program destroyed. It’s probably one of the best programs sponsored by the federal government that we’ve ever had. It does have to be made fiscally sound, but there are ways to do that without destroying the whole concept or the substance of it.”