President Obama on Saturday hammered Mitt Romney and Rep. Paul Ryan Paul Davis RyanTrump, Biden have one debate goal: Don't lose RNC chair on election: We are on track to win the White House Kenosha will be a good bellwether in 2020 MORE (R-Wis.) on two topics that could decide November's elections: Medicare and taxes.

Stumping in battleground New Hampshire, the president warned that the presumptive GOP ticket would gut Medicare at the expense of seniors and cut high-income taxes at the expense of the middle class – accusations that have only gained steam since Romney tapped Ryan as his running mate.

On both topics the president sought to draw a sharp distinction between each party's approach, with the Republicans, in his telling, showering benefits on the wealthy and Democrats fighting for everyone else.

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"The centerpiece of my opponent’s entire economic plan is a new, $5 trillion tax cut, a lot of it going to the wealthiest Americans. And his new running mate, Congressman Ryan, put forward a plan that would let Gov. Romney pay less than 1 percent in taxes each year. Here’s the kicker: he expects you to pick up the tab," Obama told an animated crowd of supporters at a high school in Windham.

"They have been trying to sell this trickle-down snake oil before," he added. "It did not work then. It will not work now."

The Romney campaign was quick to push back, accusing the president of a "false attack" on the Republicans' tax plan and warning that Obama's alternative approach – which features a tax hike on the wealthiest Americans – would cripple the ability of businesses to hire new workers.

"The fact is President Obama wants to raise taxes on private investment and job creators, which will lead to higher unemployment and fewer jobs," Ryan Williams, a Romney campaign spokesman, said in an email. "The Romney-Ryan Plan eliminates taxes for the middle class on interest, dividends and capital gains and implements pro-growth policies to deliver more jobs and more take-home pay for middle-class families."

On Medicare, the debate followed a similar arc. Obama touted the benefits of the Democrats' 2010 healthcare reform law – including provisions to cut prescription drug costs and provide free new preventive care services – while attacking the Republicans' plan for slashing seniors’ benefits to pay for tax cuts for the rich.

"Here is the bottom line: My plan saves money in Medicare by cracking down on fraud and waste and insurance company subsidies, and their plan makes seniors pay more so they can give another tax cut to millionaires and billionaires," Obama said. "My plan has already extended the life of Medicare by nearly a decade. Their plan would put Medicare on track to be ended as we know it.

"That," Obama said, "is the choice in this election."

A few hours earlier and 1,300 miles to the south, Ryan had delivered a decidedly different message. Visiting Florida for the first time since being tapped as Romney's running mate, the Wisconsin Republican told a crowd of senior citizens that it's Obama's plan for Medicare – not the Republicans' – that seniors should fear.

“Medicare was there for my family, for my grandma, when we needed it then. And Medicare’s there for my mom while she needs it now,” Ryan, appearing beside his 78-year-old mother, told the cheering crowd. "We need to keep that guarantee."

Democrats have been almost giddy at the opportunity to link Romney to Ryan's austere budgets, particularly the Medicare provisions. But Ryan on Saturday was hardly backing away from his plans for the program. Instead, he, Romney and other Republicans are attacking the roughly $700 billion in cuts to projected Medicare growth estimated under the Democrats' reform law.

"We want this debate, we need this debate, and we're going to win this debate," Ryan said.

Complicating the argument for Republicans has been the vague nature of their plans for both Medicare and taxes. Romney has endorsed Ryan's most recent budget, for instance, but more recently has backed away from it, saying he'll offer his own plan sometime in the future. Also, while Ryan’s budget repeals most of the Democrats' healthcare reforms, it keeps the more than $700 billion in Medicare cuts – the same cuts the Republicans are warning will devastate the program.

"They're being dishonest about my plan since they can't sell their plan," Obama said Saturday.

Meanwhile, Romney has said his tax plan would lower rates for all income levels, but he has yet to identify the tax loopholes he'd eliminate to cover the loss in revenues.

Attempting to fill in those blanks, the Tax Policy Center, a non-partisan policy shop, found recently that a plan like Romney's would hike taxes on those earning less than $200,000 per year, while providing generous tax breaks for those earning more.

The report has not been overlooked by Obama and Democrats, who are using it as further evidence that Republicans would give preferential treatment to the wealthy.

"Gov. Romney’s tax plan would actually raise taxes on middle-class families with children by an average of $2,000,” Obama said in New Hampshire. "Not to reduce the deficit, or grow jobs or invest in education, but to give another tax cut to people like him."

The reference to Romney's personal taxes is no accident, as Democrats have hounded the former Bain Capital CEO for weeks to release additional tax returns after a report last month detailed his use of offshore accounts.

Romney has released returns from 2010, which show him paying 13.9 percent, and an estimate of his 2011 taxes. Some critics, notably Senate Majority Leader Harry Reid Harry Mason ReidGOP senators confident Trump pick to be confirmed by November Durbin: Democrats can 'slow' Supreme Court confirmation 'perhaps a matter of hours, maybe days at most' Supreme Court fight pushes Senate toward brink MORE (D-Nev.), have suggested Romney has used tax shelters to avoid paying anything at all – a charge Romney dismissed this week.

"Every year, I’ve paid at least 13 percent,” he told reporters Thursday.

The revelation has done nothing to appease Democrats, however, who want the former Massachusetts governor to prove the claim.

"He is running for president of the United States, and he needs to hold to the precedents of recent presidential candidates in modern times who have released multiple years of tax returns," Rep. Debbie Wasserman Schultz (Fla.), head of the Democratic National Committee, told MSNBC Friday. "Because in America we don't just say ‘trust me.’"