CHARLOTTE, N.C. — In a rousing double-header, Democratic delegates heard Barack Obama and Joe Biden both accept renomination on their convention’s final night. And we heard some facts being spun.

President Obama boasted that his plan would cut the deficit by $4 trillion over 10 years, citing “independent experts.” But one such analyst called a key element of the plan a “gimmick.”

Vice President Biden quoted GOP presidential nominee Mitt Romney as saying “it’s not worth moving heaven and earth” to catch Osama bin Laden. Actually, Romney said he’d target more than just “one person.”

The president said U.S. automakers are “back on top of the world.” Nope. GM has slipped back to No. 2 and is headed for third place in global sales this year, behind Toyota and Volkswagen.

Biden said “the experts” concluded Romney’s corporate tax plan would create 800,000 jobs in other countries. One expert said that. She also said the number depends on the details, and foreign jobs could grow without costing U.S. jobs.

Obama quoted Romney as saying it was “tragic” to “end the war in Iraq.” What Romney was criticizing was the pace of Obama’s troop withdrawal, not ending a war.

Biden claimed Romney “believes it’s OK to raise taxes on middle classes by $2,000.” Romney actually promises to lower middle-class taxes.

Biden said Romney and running mate Paul Ryan “are not for preserving Medicare at all.” Actually, the plan they endorse would offer traditional Medicare as one option among many.

Obama said his tax plan would restore “the same rate we had when Bill Clinton was president” for upper-income taxpayers. Not quite. New taxes to finance the health care law also kick in next year, further burdening those same taxpayers.

$4 Trillion Deficit Reduction?

Obama exaggerated when he claimed “independent experts” say his deficit-reduction plan would reduce the federal deficit by $4 trillion over 10 years. Actually, one independent analysis criticized a central part of the president’s plan as a “gimmick.”

In September of last year, Obama released “The President’s Plan for Economic Growth and Deficit Reduction.” The plan purports to generate $4 trillion in deficit reduction over 10 years — including “more than $1 trillion in savings over the next 10 years from our drawdowns in Afghanistan and Iraq.”

In February, when Obama released his fiscal year 2013 budget, the Committee for a Responsible Federal Budget criticized the president’s plan for relying on savings from winding down the two wars. Maya MacGuineas, president of the bipartisan group, called it a “gimmick.”

“There are a number of good policies in this budget, but the use of this war gimmick is quite troubling,” said MacGuineas. “Drawing down spending on wars that were already set to wind down and that were deficit financed in the first place should not be considered savings. When you finish college, you don’t suddenly have thousands of dollars a year to spend elsewhere — in fact, you have to find a way to pay back your loans.”

In addition, the president’s plan includes another $1 trillion in savings from the Budget Control Act that had been agreed to as part of the deal with Congress to raise the debt ceiling. That’s not new savings, but accounts for already agreed-upon savings.

Biden’s bin Laden Baloney

Biden repeated the Obama campaign’s claim — previously made in a Web ad — that Romney said that “it’s not worth moving heaven and earth, and spending billions of dollars” to catch Osama bin Laden.

The claim, which Republicans disputed, fails to include the rest of Romney’s quote from an Associated Press story. Romney said the country’s focus should not be on one person, but it should be a “broader strategy to defeat the Islamic jihad movement.”

Biden: Folks, Governor Romney didn’t see things that way. When he was asked about bin Laden in 2007, here’s what he said. He said, “It’s not worth moving heaven and earth and spending billions of dollars just to catch one person.”

Romney’s quote comes from an interview with the AP in April 2007 — when bin Laden was still alive.

AP: [Romney] said the country would be safer by only “a small percentage” and would see “a very insignificant increase in safety” if al-Qaida leader Osama bin Laden was caught because another terrorist would rise to power. “It’s not worth moving heaven and earth spending billions of dollars just trying to catch one person,” Romney said. Instead, he said he supports a broader strategy to defeat the Islamic jihad movement.

A transcript of Romney’s 2007 interview, which the conservative website Townhall obtained from the Romney campaign, offers more context:

[AP reporter ] Liz Sidoti: Why haven’t we caught bin Laden in your opinion? Romney: I think, I wouldn’t want to over-concentrate on Bin Laden. He’s one of many, many people who are involved in this global Jihadist effort. He’s by no means the only leader. It’s a very diverse group – Hamas, Hezbollah, al-Qaeda, Muslim Brotherhood and of course different names throughout the world. It’s not worth moving heaven and earth and spending billions of dollars just trying to catch one person. It is worth fashioning and executing an effective strategy to defeat global, violent Jihad and I have a plan for doing that.

Not Quite ‘on Top’

The president overstated the strength of the U.S. automotive industry when he said that “we reinvented a dying auto industry that’s back on top of the world.” Not quite. General Motors has currently slipped back to No. 2 in world auto sales, based on sales for the first six months of the year, and Volkswagen is expected to push GM into third place for the full year.

GM has indeed made a comeback: It took back the top spot in global sales in 2011 after being surpassed by Toyota in 2008. Prior to that, GM had been No. 1 for more than 70 years. But for the first six months of 2012, Toyota, with 4.97 million vehicle sales, regained the lead from GM, with 4.67 million sales, for first place in worldwide auto sales. GM is expected to drop to third for all of 2012.

A Disputed Jobs Figure

Biden used a disputed figure to attack Romney’s proposal to overhaul the taxation of multinational corporations:

Biden: It’s called a territorial tax, which the experts have looked at, and they acknowledge it will create 800,000 new jobs — all of them overseas, all of them.

It’s true that one expert — Kimberly Clausing, a professor of economics at Reed College in Portland, Oregon — recently published a study calculating that a territorial system of international taxation would increase employment in low-tax countries by about 800,000 jobs. But we don’t know the details of the system Romney is proposing. The foreign job growth could be smaller, wouldn’t necessarily come at the expense of U.S. workers, and doesn’t take account of any offsetting job gains in the U.S.

Romney has proposed switching taxation of U.S.-based multinational corporations to a territorial system — in which earnings are taxed only in the countries where they are generated — similar to the system used by most other industrial nations. But Romney has not specified details, and Clausing herself said in a recent interview that the actual effect “depends on the details of the territorial system that is adopted.”

She notes in her study that “jobs abroad need not displace jobs at home” — that is, provided that the present economy improves, and U.S. unemployment drops to a low level. So depending on the economic circumstances, creating jobs overseas doesn’t necessarily mean losing jobs in the U.S., as Biden’s listeners might have assumed.

Furthermore, a critique of Clausing’s figure by the Tax Foundation (a group supported in part by corporate donations) says that she based it on current corporate tax rates — not on the lower 25 percent rate that Romney proposes. The lower rate, it is argued, would attract foreign investment and lead to importing jobs.

We won’t attempt to resolve here the merits or demerits of Romney’s embryonic corporate tax plan. The fact is that Biden quoted one study from one expert, but “experts” in general disagree.

Twisting a ‘Tragic’ Quote

Making the case that Romney lacks foreign policy chops, Obama twisted Romney’s words, claiming, “My opponent said it was ‘tragic’ to end the war in Iraq.”

But that’s not quite what Romney said. He was speaking of the speed with which Obama was withdrawing troops, not to ending the war in general.

During a veterans roundtable in South Carolina on Nov. 11, 2011, Romney criticized Obama’s plan to remove troops from Iraq by the end of that year. Here’s the fuller context of his comments, as reported by the New York Times:

Romney, Nov. 11, 2011: It is my view that the withdrawal of all of our troops from Iraq by the end of this year is an enormous mistake, and failing by the Obama administration. The precipitous withdrawal is unfortunate — it’s more than unfortunate, I think it’s tragic. It puts at risk many of the victories that were hard won by the men and women who served there.

A month earlier, when Obama formally announced the withdrawal of tens of thousands of troops from Iraq by year’s end, Romney released a similar statement:

Romney, Oct. 21, 2011: President Obama’s astonishing failure to secure an orderly transition in Iraq has unnecessarily put at risk the victories that were won through the blood and sacrifice of thousands of American men and women. The unavoidable question is whether this decision is the result of a naked political calculation or simply sheer ineptitude in negotiations with the Iraqi government. The American people deserve to hear the recommendations that were made by our military commanders in Iraq.

In December, Romney argued that Obama “has pulled our troops out in a precipitous way” and that he ought to have left a residual force of “10-, 20-, 30-thousand personnel there to help transition to the Iraqi’s own military capabilities.”

Criticizing the “precipitous” pace of withdrawal and the president’s failure to leave a residual force in Iraq is a far cry from calling the end of the war in Iraq “tragic.”

Middle-Class Taxes

Biden joined the chorus of off-key convention speakers who have attacked Romney for wanting to raise taxes on the middle class, even though Romney says he won’t do that.

Biden: Folks, Governor Romney believes it’s OK to raise taxes on middle classes by $2,000 in order to pay for … another trillion-dollar tax cut for the very wealthy.

That’s exactly the opposite of what Romney actually says. In his speech accepting the presidential nomination at the Republican National Convention, he said:

Romney, Aug. 30: I will not raise taxes on the middle class.

Biden refers to an analysis by the Tax Policy Center of a plan that, as Romney also promises, cuts income tax rates across the board by 20 percent and pays for it by eliminating and reducing tax deductions and credits. TPC found that such a plan would “increase the tax burdens on middle- and/or lower-income taxpayers.” Under one scenario, it said that “taxpayers with children who make less than $200,000 would pay, on average, $2,000 more in taxes.”

But that’s not evidence that Romney wants to increase taxes on the middle class. It only proves Romney “can’t accomplish all his stated objectives,” according to the Tax Policy Center’s director, Donald Marron.

Biden Distorts Romney’s Medicare Plan

Biden took aim at Romney’s Medicare plan, saying it would “immediately cut benefits for more than 30 million seniors” and “cause Medicare to go bankrupt by 2016.” In fact, he said, “They’re not for preserving Medicare at all.” All of those claims are misleading.

Biden: You heard them talk so much about how they cared so much about Medicare, how much they wanted to preserve it. That’s what they told you. But let’s look at what they didn’t tell you. What they didn’t tell you is that the plan they have already put down on paper would immediately cut benefits for more than 30 million seniors already on Medicare. What they didn’t tell you — what they didn’t tell you is the plan they’re proposing would cause Medicare to go bankrupt by 2016. And what they really didn’t tell you is they — if you want to know — if you want to know — they’re not for preserving Medicare at all. They’re for a new plan. It’s called “Vouchercare.”

Let’s unpack these claims one by one. When Biden says the Romney plan “would immediately cut benefits for more than 30 million seniors already on Medicare,” he’s referring to Romney’s promise to dismantle the Affordable Care Act. As part of the health care law, seniors on Medicare are entitled to free annual preventive care and increased prescription drug coverage. But Romney has not advocated cutting any of the traditional benefits provided by Medicare.

And as we wrote Sept. 6 after former President Bill Clinton made a similar claim, the Romney plan will not “cause Medicare to go bankrupt by 2016. ” But a part of Medicare — the hospital insurance trust fund — would not be able to pay full benefits for hospital services if the growth in Medicare spending is not cut, as the health care law prescribes. Physician and prescription drug benefits, financed separately out of general tax revenues and premiums, wouldn’t be affected.

As we explained in our Aug. 22 article, “A Campaign Full of Mediscare,” the Medicare hospital trust fund is on pace to be exhausted by 2024 — or by 2016 if the Affordable Care Act is repealed. But trustees estimate Medicare would still collect enough payroll taxes to fund 87 percent of the cost of hospital bills that would come due. The funding gap would continue to grow, and by 2050 the fund could cover only 67 percent of its bills. But that doesn’t mean Medicare would be “bankrupt”and would suddenly halt all payments. And if it wished, the government could make up the shortfall with tax dollars.

Biden’s claim that “they’re not for preserving Medicare at all,” is also misleading. Under the Romney/Ryan plan, those 55 and older would remain in traditional Medicare. For those currently under 55, the Romney-Ryan plan would institute a new premium-support plan beginning with new beneficiaries in 2023. Seniors would pick from private plans, or could choose traditional Medicare, all of which would be offered on a new Medicare exchange. So, those 55 and over would still get Medicare, and those under 55 could opt for traditional Medicare.

Not the Same as Clinton

Obama said he proposed a return to the same tax rate on upper-income households that prevailed during the booming economy of the 1990s. But that’s not quite accurate.

Obama: I want to reform the tax code so that it’s simple, fair, and asks the wealthiest households to pay higher taxes on incomes over $250,000 – the same rate we had when Bill Clinton was president; the same rate we had when our economy created nearly 23 million new jobs.

Obama refers to his wish to allow the Bush tax cuts to expire for families with over $250,000 annual income, or for individuals with over $200,000. The top marginal income tax rate would return to 39.6 percent, where it was set by Clinton’s 1993 tax increase, up from 35 percent, where it has been since 2003.

But that’s not the whole story. Obama has signed some new taxes to help finance the Affordable Care Act, increasing the burden on those upper-income taxpayers. Starting Jan. 1 next year, they will pay an additional 0.9 percent of wages for Medicare payroll taxes. And they will also be subject to a 3.8 percent tax on investment income from such things as stocks, bonds and sale of real estate. Those are taxes that didn’t exist when Clinton was president. If Obama succeeds in raising the top income tax rates to Clinton-era levels, total taxes on those making over $250,000 family income are thus likely to be higher than they were under Clinton. (They’ll still benefit from the Bush cuts on their income below $250,000, because Obama wouldn’t restore those lower-bracket rates to Clinton levels. So some upper-income taxpayers could still end up paying less federal tax than they paid under Clinton, depending.)

— Lori Robertson, with Brooks Jackson, Eugene Kiely, Robert Farley and Ben Finley

Correction, Sept 14: Our original story quoted Prof. Clausing’s study as saying her 800,000 figure would result from a “pure” territorial system. She has since told us her study was based on a “hybrid” system similar to those in place in other countries. We have revised our “disputed job figure” section accordingly.