ORLANDO - Maria Rubin is one of the coveted independent voters in this swing state -- so independent that she will not say whether she is voting for President Obama or Mitt Romney. She does share her age (63) and her opinion on Medicare: "I'm not in favor of changing it, or eliminating it."

Her attitude speaks to one of the biggest challenges facing the GOP ticket: countering the Democrats' longstanding advantage as the party more trusted to deal with Medicare.

In the 2010 congressional races, successful Republicans believed that they had finally found a way to do that, by linking the program's future to Obama's unpopular health insurance overhaul and accusing Democrats of cutting Medicare to pay for it. Romney resumed the offensive, joined by his running mate Paul Ryan.

But in recent weeks Obama has hit back hard, and enlisted former President Bill Clinton as well, to make the case that the GOP approach would leave older Americans vulnerable to rising health care costs.

Challenge for Republicans

At the heart of the conflict is the proposal backed by Romney and Ryan to change the way Medicare works in an effort to drive down health care costs and keep the program solvent. Under their plan, retirees would get a fixed annual payment from the government that they could use to buy traditional Medicare coverage or a private health insurance policy. Supporters say the change would hold expenses down by introducing more competition into the system.

Critics say the fixed payments might not keep up with rising insurance costs and could leave older Americans facing cutbacks in care or paying more out of pocket. Democrats contend that Medicare's rising costs can be held down within the existing system. Democrats are calling the GOP approach a "voucher" plan, suggesting that it borders on privatizing the system; Republicans prefer the term "premium support."

Challenge for Democrats

But it is a paradox of recent politics that despite Democrats' usual advantage on Medicare, voters 65 and older are the age group least supportive of Obama and his party. His challenge is to depress Romney's support among older voters by raising doubts about Republicans on Medicare.

"It's pretty clear that Medicare is the one issue that could dislodge the Republicans' headlock on those voters," said Andrew Kohut, the president of the nonpartisan Pew Research Center.

So it was no accident that Clinton's first post-convention trip as a surrogate for Obama was to Florida, where Medicare is an especially resonant issue. The 2010 health care law reduced Medicare subsidies to insurance companies to help save $716 billion over 10 years, which added eight years to the program's financial life.

Clinton pointed out that a record number of insurance companies and beneficiaries now participate in Medicare Advantage, and that premiums are lower. He said, "So if the president was trying to wreck Medicare Advantage, he did a poor job of it because it's in the best shape it's ever been in."