Laying out the first plans for his party's presidential ticket, GOP vice presidential nominee Paul Ryan took some factual shortcuts Wednesday night when he attacked President Barack Obama's policies on Medicare, the economic stimulus and the budget deficit.

Sen. Rob Portman, a former U.S. trade representative, glossed over his own problems when critiquing Obama's trade dealings with China. A day earlier, the convention's keynote speaker, New Jersey Gov. Chris Christie, bucked reality in promising that GOP presidential nominee Mitt Romney will lay out for the American people the painful budget cuts it will take to wrestle the government's debt and deficit woes under control.

And former senator and presidential candidate Rick Santorum stretched the truth in taking Obama to task over his administration supposedly waiving work requirements in the nation's landmark welfare-to-work law.

A closer look at some of the words spoken at the GOP convention in Tampa, Fla.:

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RYAN: "And the biggest, coldest power play of all in Obamacare came at the expense of the elderly. ... So they just took it all away from Medicare. Seven hundred and sixteen billion dollars, funneled out of Medicare by President Obama."

THE FACTS: Ryan's claim ignores the fact that Ryan himself incorporated the same cuts into budgets he steered through the House in the past two years as chairman of its Budget Committee, using the money for deficit reduction. And the cuts do not affect Medicare recipients directly, but rather reduce payments to hospitals, health insurance plans and other service providers.

In addition, Ryan's own plan to remake Medicare would squeeze the program's spending even more than the changes Obama made, shifting future retirees into a system in which they would get a fixed payment to shop for coverage among private insurance plans. Critics charge that would expose the elderly to more out-of-pocket costs.

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RYAN: "The stimulus was a case of political patronage, corporate welfare and cronyism at their worst. You, the working men and women of this country, were cut out of the deal."

THE FACTS: Ryan himself asked for stimulus funds shortly after Congress approved the $800 billion plan, known as the American Recovery and Reinvestment Act. Ryan's pleas to federal agencies included letters to Energy Secretary Steven Chu and Labor Secretary Hilda Solis seeking stimulus grant money for two Wisconsin energy conservation companies.

One of them, the nonprofit Wisconsin Energy Conservation Corp., received $20.3 million from the Energy Department to help homes and businesses improve energy efficiency, according to federal records. That company, he said in his letter, would build "sustainable demand for green jobs." Another eventual recipient, the Energy Center of Wisconsin, received about $365,000.

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RYAN: Said Obama misled people in Ryan's hometown of Janesville, Wis., by making them think a General Motors plant there threatened with closure could be saved. "A lot of guys I went to high school with worked at that GM plant. Right there at that plant, candidate Obama said: 'I believe that if our government is there to support you ... this plant will be here for another hundred years.' That's what he said in 2008. Well, as it turned out, that plant didn't last another year."

THE FACTS: The plant halted production in December 2008, weeks before Obama took office and well before he enacted a more robust auto industry bailout that rescued GM and Chrysler and allowed the majority of their plants — though not the Janesville facility — to stay in operation. Ryan himself voted for an auto bailout under President George W. Bush that was designed to help GM, but he was a vocal critic of the one pushed through by Obama that has been widely credited with revitalizing both GM and Chrysler.

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RYAN: Obama "created a bipartisan debt commission. They came back with an urgent report. He thanked them, sent them on their way and then did exactly nothing."

THE FACTS: It's true that Obama hasn't heeded his commission's recommendations, but Ryan's not the best one to complain. He was a member of the commission and voted against its final report.

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CHRISTIE: "Mitt Romney will tell us the hard truths we need to hear to end the torrent of debt that is compromising our future and burying our economy. ... Tonight, our duty is to tell the American people the truth. Our problems are big and the solutions will not be painless. We all must share in the sacrifice. Any leader that tells us differently is simply not telling the truth."

THE FACTS: Romney has made a core promise to cut $500 billion per year from the federal budget by 2016 to bring spending below 20 percent of the U.S. economy, and to balance it entirely by 2020.

His campaign manifesto, however, is almost completely devoid of the "hard truths" Christie promises. In fact, Romney is promising to reverse $716 billion in Medicare savings achieved by Obama over the coming decade and promises big increases in military spending as well, along with extending tax cuts for everyone, including the wealthiest.

The few specifics Romney offers include repealing Obama's health care law, cutting federal payrolls, weaning Amtrak from subsidies, cutting foreign aid and curbing the Medicaid health care program for the poor and disabled.

But it'll take a lot more than those steps for Romney to keep his vague promises, which are unrealistic if he's unwilling to touch Medicare and Social Security in the coming decade. Even the controversial budget plan of his vice presidential nominee, Rep. Paul Ryan, R-Wis., largely endorsed by Romney, leaves Medicare virtually untouched over the next 10 years.

What's left for Romney to cut is benefit programs other than Medicare and Social Security, which include food stamps, welfare, farm subsidies and retirement benefits for federal workers. The remaining pot of money includes the day-to-day budgets of domestic agencies, which have already borne cuts under last year's budget deal. There's also widespread congressional aversion to cutting most of what remains on the chopping block, which includes health research, NASA, transportation, air traffic control, homeland security, education, food inspection, housing and heating subsidies for the poor, food aid for pregnant women, the FBI, grants to local governments, national parks and veterans' health care.

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PORTMAN: "Take trade with China. China manipulates its currency, giving it an unfair trade advantage. So why doesn't the president do something about it? I'll tell you one reason. President Obama could not run up his record trillion-dollar deficits if the Chinese didn't buy our bonds to finance them. Folks, we are as beholden to China for bonds as we are to the Middle East for oil. This will end under Mitt Romney."

THE FACTS: Portman is an expert on commerce, having served as President George W. Bush's trade representative from May 2005 to May 2006. But he didn't fare particularly well in stemming China's trade advantage, either.

Under Portman's watch, the U.S. trade deficit with China soared by 25 percent in 2005, and the next year it climbed more than 15 percent. By contrast, the deficit rose 10 percent over the first three years of Obama's presidency, according to U.S. government figures.

Both the Bush and Obama administrations have launched unfair trade cases against China at the World Trade Organization, but neither has been able to rebalance the relationship.

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SANTORUM: "This summer (Obama) showed us once again he believes in government handouts and dependency by waiving the work requirement for welfare. Now, I helped write the welfare reform bill. We made a lot crystal clear. No president can waive the work requirement, but as with his refusal to enforce our immigration laws, President Obama rules like he is above the law."

THE FACTS: The administration did not waive the work requirement. Instead, it invited governors to apply on behalf of their states for waivers of administrative requirements in the 1996 law. Some states have complained those rules tie up caseworkers who could be helping clients directly.

In a July 18 letter to congressional leaders, Health and Human Services Secretary Kathleen Sebelius said that to be eligible for a waiver, governors must commit that their plans will move at least 20 percent more people from welfare to work. Moreover, states must show clear progress toward the goal within a year, or lose the waiver.

"We will not accept any changes that undercut employment-focused welfare reforms that were signed into law fifteen years ago," Sebelius wrote.

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Ron Haskins, a former senior Republican House aide who helped write the welfare-to-work law, has said "there is merit" to the administration's proposal and "I don't see how you can get to the conclusion that the waiver provision undermines welfare reform and it eliminates the work requirement."

Haskins, now co-director of the Brookings Center on Children and Families, says the administration was wrong to roll out its proposal without first getting Republicans to sign off on it. But he said the idea itself is one both parties should be able to agree on, were it not for the bitter political divisions that rule Washington.