WASHINGTON -- President Obama remains more trusted to address Medicare's challenges, the latest USA TODAY/Gallup Poll of Swing States shows, even as Mitt Romney challenged him over the issue Thursday in retiree-rich Florida.

In the nation's 12 top battlegrounds, including the Sunshine State, voters by 50%-44% say they have more faith in Obama than his Republican challenger on Medicare. They are slightly more likely to say Romney is proposing changes that would weaken the nation's health care system for seniors.

There is a wider accord on another question: By 53%-44%, most are pessimistic that Medicare will still be providing all Americans over 65 with adequate health care coverage 20 years from now.

At a rally in Sarasota, Romney blasted Obama for trimming $716 billion from the Medicare Advantage program as part of the Affordable Care Act signed two years ago. "What he has done to Medicare to pay for Obamacare is wrong," Romney said to cheers. Romney's plan, akin to one authored by his running mate, Paul Ryan, would convert the entitlement program to one that would give seniors a subsidy to buy coverage.

Romney raised the issue at the rally -- in case anyone missed the point, he stood in front of a huge sign that read "Protect & Strengthen Medicare" -- and began airing a new TV ad in Florida that defends the GOP proposal for significant change.

"Mitt Romney and Paul Ryan get it: Medicare is going broke," Florida Sen. Marco Rubio says in the ad, mentioning his own 81-year-old mother as evidence of his commitment to the program. "That's not politics; it's math."

The Obama campaign also is airing ads on Medicare, including one unveiled last week. "Fact: Barack Obama will protect your guaranteed benefits and will not allow Medicare to become a voucher program," the narrator says. "Fact: Mitt Romney would take away Medicare as guaranteed benefits and instead give future retirees 'premium support' or vouchers."

Separately, the SEIU Thursday began airing a radio ad in Florida that features an anxious senior asking her son about conflicting TV ads on Medicare. He warns that the Romney-Ryan plan "does essentially end Medicare" -- a charge disputed by independent analysts. "I don't like the sound of that," she replies.

That sort of message resonates with Lucy Hill of Philadelphia, at age 69 a Medicare beneficiary. She was among those called in the USA TODAY poll. "The Republicans -- it's very frightening to me what they might do with it," she said in a follow-up phone interview. "I really do think we can trust that it won't be changed significantly with Obama."

Norma Hagarman, 76, of Greenacres, Fla., has a different view. "I think that maybe what Romney has planned for it, maybe that will be the way to go," she said, saying competition among insurance companies could drive down what she sees as "crazy costs" for the government and beneficiaries.

The swing states surveyed were Colorado, Florida, Iowa, Michigan, Nevada, New Hampshire, New Mexico, North Carolina, Ohio, Pennsylvania, Virginia and Wisconsin. The poll of 1,096 registered voters, taken Sept. 11-17, has a margin of error of +/- 4 points.

In the poll, voters:

Are inclined to say Obama has put forward a specific plan for Medicare, 51%-46%, while they don't think Romney has done so, 50%-44%. This response and those on other questions seem shaped in large part by partisan perspective: 89% of Democrats say Obama has a plan; 74% of Republicans say Romney does.

Are divided by the impact of Obama's plan: 33% say it would strengthen the program, 32% weaken it. The assessment of Romney's plan is a bit more negative: 31% say it would strengthen the program, 36% weaken it.

Differ by age on which candidate they trust more to address Medicare's challenges. Those 65 and older, Romney's strongest age group, trust him more by 50%-41%. But those under 30, Obama's strongest age group, trust the president more, 67%-25%.

At stake in the debate could be the outcome in such closely divided battleground states as Florida, New Hampshire and Iowa that have senior-heavy electorates especially sensitive to issues such as Medicare and Social Security. Democratic pollster Mark Mellman says the decision to engage on Medicare is a gamble the GOP is losing.

"This is still a tremendous disadvantage for Republicans," he says. "They thought they could fight it to a complete draw. They haven't even gotten it any closer." While the margin on who is more trusted is just six percentage points, he notes that is four points wider than Obama's 48%-46% lead in the Swing States poll. "The fact that we're doing better on Medicare than on the partisan split is pretty good."

Republican pollster David Winston disputes that, saying Republicans have succeeded in narrowing what traditionally has been a double-digit Democratic lead on health care issues including Medicare. "Now we're still behind but six points is significantly better than being minus 25," he says. "That's an improvement."

It is an issue on which neither side scores very well, he adds. "The country is still waiting for somebody to come up with a solution that will work. That will end up making it a draw -- which for Republicans is a good outcome."

USA Today