WASHINGTON — In the rough-and-tumble of a town hall-style debate, not all the presidential candidates’ claims stood up to scrutiny Tuesday.

Yet again, President Barack Obama claimed that ending the Afghanistan and Iraq wars makes money available to “rebuild America,” even though it doesn’t. And he pointed to a string of job creation while ignoring the job losses that came before it, on his watch.

Republican Mitt Romney actually corrected some of the errant claims he’s made before, while stretching the facts on the auto bailout he opposed.A look at some of their claims:

OBAMA: “Let’s take the money that we’ve been spending on war over the last decade to rebuild America, roads, bridges, schools. We do those things, not only is your future going to be bright, but America’s future is going to be bright as well.”

THE FACTS: What Obama didn’t mention is that much of the money that has been paying for the wars in Iraq and Afghanistan was borrowed. The government borrows nearly 40 cents for every dollar it spends. Thus using money that had been earmarked for wars to build schools and infrastructure would involve even more borrowing, adding to the federal deficit.

ROMNEY: “I know he keeps saying, ‘You want to take Detroit bankrupt.’ Well, the president took Detroit bankrupt. You took General Motors bankrupt. You took Chrysler bankrupt. So when you say that I wanted to take the auto industry bankrupt, you actually did. And I think it’s important to know that that was a process that was necessary to get those companies back on their feet, so they could start hiring more people. That was precisely what I recommended and ultimately what happened.”

THE FACTS: What Romney recommended did not happen, and his proposed path probably would have forced GM and Chrysler out of business. He opposed using government money to bail out the automakers, instead favoring privately financed bankruptcy restructuring. But the automakers were bleeding cash and were poor credit risks. The banking system was in crisis. So private loans weren’t available. Without government aid, both companies probably would have gone under.

OBAMA: “And what I want to do is build on the 5 million jobs that we’ve created over the last 30 months in the private sector alone.”

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THE FACTS: As he has done before, Obama is cherry-picking his numbers to make them sound better than they really are. He ignores the fact that public-sector job losses have dragged down overall job creation. Also, he chooses just to mention the last 30 months. That ignores job losses during his presidency up until that point. According to the Labor Department, about 4.5 million total jobs have been created over the past 30 months. But some 4.3 million jobs were lost during the earlier months of his administration. Obama is a net job creator, but marginally.

ROMNEY: “The proof of whether a strategy is working or not is what the price is that you’re paying at the pump. If you’re paying less than you paid a year or two ago, why, then, the strategy is working. But you’re paying more. When the president took office, the price of gasoline here in Nassau County was about $1.86 a gallon. Now, it’s $4.00 a gallon. The price of electricity is up. If the president’s energy policies are working, you’re going to see the cost of energy come down.”

THE FACTS:When Obama took office, the world was in the grip of a financial crisis and crude prices had plummeted because world demand had collapsed. Other energy prices have fallen during Obama’s term. Electricity prices, when adjusted for inflation, are down, and homeowners are finding it much cheaper to heat their homes with natural gas. That’s because natural gas production has surged, reducing prices both for homeowners and for utilities that burn gas to generate electricity.