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Obama and Vice President Joe Biden have released their returns for the years since 2000. The Obamas paid 20.5 percent in federal income taxes in 2011.
Ryan, meanwhile, found himself doing his own explaining.
He and Romney have launched a new strategy this week of criticizing Obama for taking more than $700 billion in Medicare funds to help pay for his health care overhaul. Yet those same cuts are in a House Republican budget blueprint authored by Ryan.
A reporter pressed him on the issue during a stop at a hot dog restaurant in Warren, Ohio.
His explanation was that the Medicare cuts were part of the existing baseline budget, including the Obama health care law he opposes.
"It gets a little wonky, but it was already in the baseline," Ryan said. "We would never have done it in the first place."
Romney hadn't scheduled any public events but put together a last-minute news conference to explain the differences between his Medicare plan and Obama's.
"Which of these two do you think is better?" Romney asked as he stood under a glaring sun at an airport.
Romney says Obama has cut $716 billion from the Medicare trust fund to pay for his national health care overhaul, weakening the program. Those cuts, mostly from health providers and insurance plans instead of directly from beneficiaries, would decrease the cost of the entitlement program over time and extend the life of the trust fund.
Ryan's budget would make those same cuts, though he would use the savings differently.
Romney — and Ryan, since joining the ticket — insist the cuts must be restored. That could make Medicare go bankrupt more quickly. But Romney says other parts of his plan, including giving fewer benefits to wealthier retirees, would keep Medicare solvent in the long term.
Independent groups say he has not supplied enough details to determine whether he would significantly shore up Medicare in years to come.
Democratic strategists and party officials say that while they still expect the race to stay close through the fall, they sense a slight shift in Obama's favor over the past two weeks. However, they expect Romney to get a boost following his party's convention and say a dismal economic report right before the election could pull votes his way.
Obama spent the day in White House meetings save for a stop at Democratic National Committee headquarters. Romney is devoting most of this week, and much of next week, to raising money in non-competitive states including Alabama, South Carolina, Massachusetts, New York, Texas, Louisiana and New Mexico.