Fact-checking the second presidential debate

President Obama and Mitt Romney met for a contentious second presidential debate Tuesday night at Hofstra University in Hempstead, N.Y. The candidates fielded questions from undecided voters in the audience, answering on topics including the attack on the U.S. Consulate in Benghazi, domestic energy production, job creation and the auto bailout. Below, CBSNews.com looks at how their assertions hold up.

LIBYA

OBAMA: "The day after the attack, governor, I stood in the Rose Garden and I told the American people in the world that we are going to find out exactly what happened. That this was an act of terror and I also said that we're going to hunt down those who committed this crime.

And then a few days later, I was there greeting the caskets coming into Andrews Air Force Base and grieving with the families.

"And the suggestion that anybody in my team, whether the Secretary of State, our U.N. Ambassador, anybody on my team would play politics or mislead when we've lost four of our own, governor, is offensive. That's not what we do. That's not what I do as president, that's not what I do as Commander in Chief."

ROMNEY: "You said in the Rose Garden the day after the attack, it was an act of terror. It was not a spontaneous demonstration, is that what you're saying?... I want to make sure we get that for the record because it took the president 14 days before he called the attack in Benghazi an act of terror... The administration indicated this was a reaction to a video and was a spontaneous reaction..."

In Sept. 12 remarks in the White House Rose Garden reacting to the Libya attack, Mr. Obama did refer generally to "acts of terror," though he didn't specifically call the attack on the U.S. consulate in Benghazi an act of terrorism.

Candy Crowley takes on Romney: Did Obama call Libya attack act of "terror"?

"No acts of terror will ever shake the resolve of this great nation, alter that character, or eclipse the light of the values that we stand for," Mr. Obama said. "Today we mourn four more Americans who represent the very best of the United States of America. We will not waver in our commitment to see that justice is done for this terrible act. And make no mistake, justice will be done."

It's true that the administration, including U.S. Ambassador to the United Nations Susan Rice, maintained for several days that the attack was spontaneous and the result of protests over an inflammatory anti-Muslim video. Meanwhile, CBS News reported on Sept. 12 that the assault appeared to be a planned terrorist attack.

In his speech to the U.N. General Assembly on Sept. 25, Mr. Obama did not give any indication that the attack was an act of terrorism, instead repeatedly referencing the anti-Muslim YouTube video that allegedly spurred spontaneous protests.

ENERGY

OBAMA: "We have increased oil production to the highest levels in 16 years. Natural gas production is the highest it's been in decades. We have seen increases in coal production and coal employment. But what I've also said is we can't just produce traditional sources of energy. We've also got to look to the future. That's why we doubled fuel efficiency standards on cars. That means that in the middle of the next decade, any car you buy, you're going to end up going twice as far on a gallon of gas. That's why we doubled clean -- clean energy production like wind and solar and biofuels..."

The American Enterprise Institute earlier this month cited the same statistic as Mr. Obama: U.S. field production of crude oil reached a 17-year high this month, when nearly 6.6 million barrels were produced domestically per day, according to the Department of Energy's Energy Information Administration (EIA). The last time production was that high was in 1995.

The EIA reported this summer that natural gas reserves reached a new high in 2010 after 12 consecutive years of increases. However, coal production has been lower during the Obama administration than it was in the previous administration. Coal mine employment was 86,195 mine employees in 2010, a 1.8-percent-drop from the 2009 level of 87,755.

The president did double fuel efficiency standards for cars, and wind and solar energy production did double between 2008 and 2011.

Obama, Romney spar on oil production

ROMNEY: "The president's right in terms of the additional oil production, but none of it came on federal land. As a matter of fact, oil production is down 14 percent this year on federal land, and gas production was down 9 percent. Why? Because the president cut in half the number of licenses and permits for drilling on federal lands, and in federal waters.

"So where'd the increase come from? Well a lot of it came from the Bakken Range in North Dakota. What was his participation there? The administration brought a criminal action against the people drilling up there for oil, this massive new resource we have. And what was the cost? 20 or 25 birds were killed and brought out a migratory bird act to go after them on a criminal basis.

"We're going to bring that pipeline in from Canada. How in the world the president said no to that pipeline? I will never know."

Romney is correct that in 2011 oil production was, in fact, down on federal lands: The EIA reported this year that "total crude oil sales of production from Federal and Indian lands increased from 642 million barrels in FY 2009 to 739 million barrels in FY 2010, but decreased to 646 million barrels in FY 2011." That amounts to an 11 percent reduction. The EIA explained that crude oil production from federal lands is "dominated by offshore production from the Federal Outer Continental Shelf" -- production that was disrupted by the Deepwater Horizon oil spill.

Romney said production was down because "the president cut in half the number of licenses and permits for drilling on federal lands, and in federal waters." But according to the Bureau of Land Management, the government issued 2,188 new leases in 2011, up from 1,308 in 2010. That's a decrease, however, from the 3,499 new leases issued in 2007. If one considers the total number of leases in effect, the number decreased slightly from 2010 (50,544 leases) to 2011 (49,173). However, there were more leases in effect in 2011 than in 2007, when there were 48,933.

The Bakken Range in North Dakota has seen a boom in oil production, and as Romney said, federal prosecutors did charge oil companies in the Bakken region for the deaths of a few migratory ducks under the Migratory Bird Treaty Act. But a federal judge early this year tossed out the charges.

JOB CREATION

ROMNEY: "We have fewer people working today than we had when the President took office."

Just before President Obama took office in January 2009, the unemployment rate was 7.8 percent.

Today, the unemployment rate again stands at 7.8 percent.

The most recent data from the Bureau of Labor Statistics indicates that, as of October 2012, for the first time in his presidency, President Obama has presided over net job creation - that is, there have been more jobs generated during his term than jobs lost during his term.

Between January 2009 and February 2010, a month recognized as the nadir of unemployment in the downturn, the American economy shed 4.3 million jobs. However, between February 2010 and today, the economy recovered 4.4 million jobs.

However, the total number of Americans on non-farm payrolls in January 2009 stood at 133.56 million. By the end of September 2012, that number was 133.50 million, a decrease of 0.06 million.

So while President Obama can legitimately claim that he has overseen a turnaround that has created more jobs than were lost in the recession, Gov. Romney is technically correct in asserting that fewer Americans are working today than when President Obama took office.

Absent in Romney's charge was a recognition that many of the job losses early in Obama's term occurred before the president's policies were able to take effect. The president and his team have argued that we should measure employment from February 2010 going forward - a cherry-picked timeline that may nonetheless provide a fairer read on the job creation record of the Obama administration.

AUTO BAILOUT

OBAMA: "[Romney] wanted to take [the auto companies] into bankruptcy without providing them any way to stay open."

President Obama seemed to refer to Romney's desire to push the auto industry into bankruptcy without providing government loans to keep the industry afloat during the restructuring.

In an op-ed written for the New York Times, Romney argued that the auto companies should undergo a managed bankruptcy process, cutting dead weight to emerge leaner and more competitive going forward. However, he also argued that the government should not loan money to the beleaguered companies, saying that private money should be provided to help them stay afloat during restructuring. He even argued that a federal auto bailout would ultimately kill the companies by forestalling the hard decisions necessary to save the industry, saying that if the government loaned money to the big three, we could "kiss the American automotive industry goodbye."

Romney, Obama battle over letting "Detroit go bankrupt"

However, the opposite may be true: if the government did not loan money to the auto companies, they may not still exist in their current form. As has been documented by many analysts, at the time of the auto bailout, there were no private financiers willing to step in and loan money to the auto companies -- it simply was not a safe investment for banks and other lenders who were still struggling through a credit crunch. The government, recognizing itself as the lender of last resort, stepped in to prop up the companies while they regrouped.

Without the infusion of government cash, a "managed bankruptcy" may have more closely resembled a liquidation process in which each company was broken into constituent pieces and sold to the highest bidder, effectively killing the American auto industry as we recognize it today.

So when President Obama claimed that Romney would have forced them into bankruptcy "without providing them any way to stay open," he was correct - and Romney's own words prove as much.