Health care and Medicare are two of the most important issues to voters in three battleground states—and voters trust that President Obama is the man to handle those issues over Mitt Romney.

Voters in Florida, Wisconsin and Ohio say the economy, health care and Medicare are "extremely important" in regard to how they'll cast their votes this November, according to a new Quinnipiac University/CBS News/New York Times poll.

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Medicare has earned a place back in the spotlight after Romney chose Paul Ryan as his running mate, who is known for his proposals to overhaul Medicare.

Most likely voters (about 60 percent) in each state say they want Medicare to continue providing health insurance to seniors the way it does now. Fewer than a third of those polled think Medicare should be changed to a system in which the government gives the elderly fixed amounts of money to buy health insurance or Medicare insurance.

This echoes the same findings of a Pew Research Center survey out earlier this week that found most Americans oppose the Medicare voucher plan.

Most also say Medicare is worthy of taxpayer dollars. Still, most voters say they'd support some reductions—but would oppose major ones—to the government program to help reduce the federal budget deficit.

But while voters say they trust Obama to better handle health care and Medicare, the poll finds voters in all three states disapprove of Obama's Patient Protection and Affordable Care Act, albeit by small margins. Those who say they don't like the law say they "strongly disapprove" by a wide majority as opposed to only "somewhat disapprove."

Approval of the PPACA breaks down by political affiliation, as well: Most Obama supporters support the law, while Romney supporters oppose it.

Even though the PPACA has been a constant source of debate, few actually think health reform will have an effect on them. Only one in five voters think the law will help them personally, while more than one-third of those voters think it will hurt them.

Though health matters belong to Obama, Romney has the edge in Florida and Wisconsin on the economy. The two are tied among Ohio voters. Romney also has the leg up on fixing the budget deficit.

Overall, voters in all the swing states said their vote belongs to Obama, but Romney trailed by only a few percentage points.

The survey was conducted from Aug. 15-21. The number of likely voters interviewed in each state is 1,241 in Florida, 1,253 in Ohio and 1,190 in Wisconsin.

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