(CNN) -- President Barack Obama and GOP vice presidential nominee Paul Ryan on Friday traded sharp criticism over health care reforms and Medicare, with each telling a leading advocacy group for senior citizens that the other was being untruthful.
"Contrary to what you've heard and what you may hear from subsequent speakers, Obamacare actually strengthened Medicare," the president told the AARP Liffe@50+ event, using the nickname for the 2010 Affordable Care Act that passed with no Republican support.
In particular, he called the claim by Ryan and other Republicans that $716 billion is being cut from Medicare to fund the health care bill "simply not true."
Ryan spoke to the same event shortly afterward, saying that Obama's contention that the health care law strengthened Medicare was "just not true," adding that the legislation "turned Medicare into a piggy bank for Obamacare."
The debate over Medicare is a major issue in the November election campaign, especially in the vital battleground state of Florida with its large population of senior citizens.
Ryan headed to Florida later Friday, while Obama campaigned in Virginia, Vice President Joe Biden spoke in New Hampshire and GOP presidential nominee Mitt Romney headed to Las Vegas. All four states are considered up-for-grabs in the election less than seven weeks away.
In a separate development, Romney released details of his 2011 income tax return that showed he made $13.7 million last year and paid $1.94 million in federal taxes, giving him an effective tax rate of 14.1%, his campaign said.
The majority of the candidate's income last year came from his investments, Brad Malt, the trustee of Romney's blind trust, said in a blog post. The Romneys gave just over $4 million to charity.
In addition, the Romney campaign said his tax filings from 1990 to 2009 show that he and his wife paid 100% of the federal and state income taxes they owed and that their overall average annual effective federal tax rate was 20.2%.
Romney has been criticized by Democrats and even some Republicans for not releasing more than two years worth of taxes. His wealth and investment industry background, as well as his father's decision to release a dozen years of tax records during his presidential run four decades ago, have only raised interest in Romney's returns.
Obama deputy campaign manager Stephanie Cutter said in a statement the disclosure "continues to mask Romney's true wealth" and income from the private equity firm he once led, leaving the American people in the dark about critical details of his finances.
Senate Majority Leader Harry Reid, D-Nevada, called the new tax information insufficient.
"What we don't know is why he refuses to be straight with the American people about the choices he's made in his financial life," according to a statement from Reid, who previously created a stir when he alleged Romney paid no taxes in some years but refused to divulge the source of his accusation.
"When will the American people see the returns he filed before he was running for president?" Reid asked.
Obama responds to health care attacks
In his appearance by satellite at the AARP event in New Orleans, Obama responded to specific attacks on the health care law by Ryan and other Republicans, declaring the 2010 measure cuts waste and fraud in Medicare, provides preventive care to keep people healthier and reduces prescription drug costs for seniors.
Savings come from "using the purchasing power of Medicare to say to doctors and hospitals and insurance companies: 'You guys need to work smarter,'" Obama said to applause. "Instead of having five different tests that each of you is charging for, do one test and email it to everybody."
Ryan, the conservative House Budget Committee chairman from Wisconsin, has proposed a partial privatization of the entitlement that would provide government subsidies to help senior citizens pay for coverage they would choose from a list of options.
He defended the plan Friday in the face of a mixed reception.
"The first step to a stronger Medicare is to repeal Obamacare because it represents the worst of both worlds," Ryan said to loud booing. He added: "I had a feeling there'd be mixed reaction so let me get into it ."
"It weakens Medicare for today's seniors and puts it at risk for the next generation," Ryan said, repeating the factually challenged claim of $716 billion in Medicare cuts and also targeting a panel created under the health care law charged with recommending ways to reach targeted savings starting in 2014.
Ryan also took a swipe at Obama's re-election slogan of "Forward," saying it means "Forward into a future where seniors are denied the care they earned because a bureaucrat decided it wasn't worth the money."
In his remarks, Obama argued that Medicare savings come from "using the purchasing power of Medicare to say to doctors and hospitals and insurance companies: 'You guys need to work smarter."
"Instead of having five different tests that each of you is charging for, do one test and email it to everybody," he said to applause.
With polls showing Romney unable to overtake Obama with less than seven weeks to go until the November election, GOP infighting is showing a rising frustration over the candidate's campaign against a president saddled by high unemployment and a sluggish economy.
New figures show Obama and his allies raised nearly $85 million in August, outpacing Romney's haul in the month that included both parties' national conventions.
In Wisconsin, conservative candidate Tommy Thompson put some of the blame for his slipping poll numbers on the Romney campaign and conservative commentators, including former GOP speechwriter Peggy Noonan, have depicted the Romney team as floundering.
"Stop it. This is hard. You want to try it? Get in the ring," Ann Romney said of her husband's critics in an interview on Thursday with Radio Iowa.
Romney tweaked his campaign strategy twice this week in response to controversies that distracted from his main message challenging Obama's record as president.
On Thursday, he kept up attacks on Obama over a 1998 comment regarding redistribution of wealth, and also claimed the president had given up on changing Washington. The Obama camp fired back that the criticism was off base.
At the AARP event Friday, Obama said the Ryan proposal to reform Medicare would make it a voucher program that shifts health care costs to senior citizens. He noted that AARP supported the 2010 health care reform act and opposed Ryan's Medicare proposal.
"They know that a voucher program is not going to be a good deal," Obama said.
Ryan, however, denied it was a voucher program and insisted that the idea originated in Democratic proposals of the past.
"This financial support system is designed to guarantee that seniors can always afford Medicare coverage -- no exceptions," he said to some applause.
Members of AARP -- a nonprofit organization and a powerful lobbying group that boasts of having more than 37 million members -- submitted questions to the nominees on their website.
Tough stretch for Romney
Romney is coming off a tough stretch in the weeks before the three presidential debates in October.
Last week, the Romney campaign struggled in its initial response to anti-American violence in Libya and Egypt. Then a left-leaning magazine released secretly recorded clips of Romney speaking at a May fund-raiser in which he said 47% of Americans depended on government help, saw themselves as victims and won't support him.
Under criticism for the comments at the fund-raiser, Romney stuck by them and rallied some conservative commentators to his side by emphasizing his message on his allegation that Obama's polices increased public dependency on government.
In particular, they accused Obama of favoring wealth redistribution -- code for socialism among conservatives -- based on the 1998 video of the president when he was a state senator in Illinois.
"I think the trick is figuring out how do we structure government systems that pool resources and hence facilitate some redistribution -- because I actually believe in some redistribution, at least at a certain level to make sure that everybody's got a shot," Obama says in the clip, posted Tuesday on the conservative Drudge Report website.
The White House on Wednesday characterized the GOP attacks over the redistribution comment as an effort to divert attention from Romney's remarks at the May fundraiser.
Romney also took aim at Obama's comment on Thursday at a Univision "Meet the Candidates" forum in which the president said he was unable to change Washington from within.
House Speaker John Boehner continued the Romney attack line on Friday, saying Obama and congressional Democrats lacked the leadership qualities necessary to change the culture of partisan divide and legislative gridlock.
"It takes courage, it takes determination and it takes sincerity, and it's called leadership," Boehner told reporters.
Asked about the inability to work out compromises with Republicans on deficit reduction and other major issues, Obama blamed GOP intransigence and said he was being a leader by rejecting what he called "bad ideas."
He noted that his proposals, including the health care reform measure opposed by every Republican, included some ideas with GOP origins.
"Obamacare owes a debt to what was done in Massachusetts by my opponent, Mr. Romney, even though sometimes he denies it," the president said in a jab at his challenger, who passed a similar plan while governor of the state but now vows to repeal the federal version.
"The one thing I won't do though is go along with bad ideas that are not helping the middle class," Obama said to applause, adding: "If I hear the only way Republicans in Congress are willing to move forward is to voucherize Medicare, I'll say no."
CNN's Shawna Shepherd, Paul Steinhauser, Dana Davidsen, Peter Hamby and Gregory Wallace contributed to this report.