NBC News takes a deep dive into the statements made by President Barack Obama and Republican presidential nominee Mitt Romney in their second debate of the 2012 election cycle. 

We take a look at two topics, the auto bailout and energy production, and put their comments to the test.

Oil and gas production on federal lands
Romney claimed that both oil and natural gas production on federal land has decreased, with Obama maintaining that the Republican’s assertions are “ just not true.”

Here’s their contentious exchange:

ROMNEY: As a matter of fact, oil production is down 14 percent each year on federal land and gas production is down 9 percent. Why?  because the president cut in half the number of licenses and permits for drilling on federal land and in federal water.
OBAMA: Here's what happened. You had a whole bunch of oil companies who had leases on public lands that they weren't using. So what we said was, you can't just sit on this for 10, 20, 30 years, decide when you want to drill, when you want to produce, when it's most profitable for you. These are public lands. So if you want to drill on public lands, you use it or you lose it.  
ROMNEY: OK –  (inaudible) –
OBAMA: And so what we did was take away – 
ROMNEY: That's –
OBAMA: –  those leases, and we are now re-letting them so that we can actually make a profit. 
ROMNEY: And  – and –  and production on private –  on government lands is down. 
OBAMA: And the production is up. No it isn't. 
ROMNEY: Production on government land of oil is down 14 percent. 
OBAMA: Governor –  
ROMNEY: And production of gas is down 9 percent.  
OBAMA: What you're saying is just not true. It's just not true.
ROMNEY: I  –  it's absolutely true. 

What’s the truth? Oil production did fall by 14 percent on federal lands - onshore and offshore -  but that was only in one year, from 2010 to 2011.

And it was mainly the result of fallout from the Deepwater Horizon oil spill in the Gulf of Mexico in 2010.

But Obama is correct, that since he took office, oil production on federal lands is up.

RELATED: Sharp exchanges at second debate

In both 2009 and 2010, oil production increased ... so even with the 14 percent drop last year, overall production on federal land is still up 10.6 percent since 2008. 

But natural gas production on federal lands is down, and has been declining since 2003, according to the Energy Information Administration, mainly because of a decline in offshore natural gas drilling. 

Charles Dharapak / AP

President Barack Obama and Republican presidential candidate and former Massachusetts Gov. Mitt Romney participate in the second presidential debate at Hofstra University in Hempstead, N.Y.

Auto bailout
Obama called out Romney for not backing measures to save troubled car companies – the former Massachusetts governor opposed the federal bailout.

VOTE: Did the second presidential debate do anything to influence who you will support in the election?

"Now when Gov. Romney said we should let Detroit go bankrupt. I said we're going to bet on American workers and the American auto industry and it's come surging back."

The president was referring to a newspaper piece Romney wrote back in 2008, but the governor never actually said, “Let Detroit go bankrupt.”

The New York Times wrote that headline, not Gov. Romney. 

Romney did say the auto companies should go through what’s called a “managed bankruptcy,” where the companies would get help from private investors but not taxpayers’ money.

Slideshow: On the campaign trail

Reuters, Getty Images

In the final push in the 2012 presidential election, candidates Mitt Romney and Barack Obama make their last appeals to voters.

Launch slideshow

Ryan accused the Obama administration of not properly protecting the ambassador.

“What we should not be doing is rejecting claims for calls for more security in our barracks we need marines in Benghazi when the commander on the ground says we need more forces for security there were requests for extra security, those requests were not honored,” Ryan said.

Biden called the deaths a tragedy, but he then claimed that the Obama administration did not know that the ambassador and other  personnel on the ground had been more asking for more security.

“We weren't told they wanted more security,” Biden said. “We did not know they wanted more security men and, by the way, at the time, we said exactly what the intelligence community told us that they knew, that was the assessment."

But the State Department did know that requests for more security resources had been made and were turned down.  A State Department official acknowledged that testifying Wednesday on Capitol Hill.

"Imagine had we let the Republican Congress work out the sanctions," said Biden. "You think there's any possibility the entire world would have joined us, Russia and China, all of our allies? These are the most crippling sanctions in the history of sanctions. Period."

Biden is mostly correct: the administration did marshal international support for the most crippling sanctions, although they did not want to sanction Iran's central bank until Congress forced the president to do so.

Spending
Biden accused Ryan of being a big government spender.

Ryan voted for the Bush tax cuts, the wars in Iraq and Afghanistan, and the expansion of Medicare to cover prescription drugs -- all of which Biden says added to the deficit.

“And, by the way, they talk about this Great Recession if it fell out of the sky, like, ‘Oh, my goodness, where did it come from?’” Biden said. “It came from this man voting to put two wars on a credit card, to at the same time put a prescription drug benefit on the credit card, a trillion-dollar tax cut for the very wealthy. I was there. I voted against them. I said, no, we can't afford that.”

But looking at Biden’s own Senate votes, he voted for an early version of that Medicare prescription drug coverage. But later, Biden did not support the final Medicare drug benefit that President George W. Bush signed into law.

And the vice president was incorrect when he suggested tonight that he did not support the two wars because the country could "not afford" them. Biden voted for both wars.

Medicare
There was a sharp disagreement over Medicare. Biden charged that Ryan’s original plan would raise out-of-pocket costs.

“Look, folks, use your common sense,” Biden said. “Who do you trust on this -- a man who introduced a bill that would raise it 40 -- $6,400 a year; knowing it and passing it, and Romney saying he'd sign it, or me and the president?”

Ryan objected.

Updated at 10:55 p.m. ET

Social Security
Tonight, President Barack Obama made a claim about Social Security.

OBAMA: Social Security is structurally sound, it's gonna have to be tweaked the way it was by Ronald Reagan and Speaker, Democratic Speaker Tip O'Neill. But it is, the basic structure is sound.

President Obama said that, unlike Medicare, Social Security does not need to be fundamentally fixed to remain solvent.

But according to the Congressional Budget Office, Social Security will run into financial trouble, too -- about 20 years from now.

By the year 2030, the amount Social Security pays out will exceed the tax revenue coming in -- so in about 20 years the program will NOT be able to pay for itself through the payroll taxes Americans currently pay.

Medicare
Mitt Romney claimed President Obama's health care law would take $716 billion out of Medicare.

ROMNEY: What I support is no change for current retirees and near-retirees to Medicare. And the president supports taking $716 billion out of that program.

In fact, that $716 billion comes from trimming planned future increases over the next decade, not cutting funding. And those trims come from limiting payments to health-care providers and insurers -- NOT limiting care to seniors.

And Medicare's chief actuary says Obama's health reform "substantially improves" the program's finances.

Romney's claim that his plan would not change anything for seniors and near retirees is true. His changes would not affect anyone currently over the age of 55.

What would happen for younger Americans under Romney's plan?

Has essentially endorsed the latest version of the Ryan budget plan, which substantially transforms Medicare by giving future seniors a payment -- Democrats call it a “voucher,” Republicans call it “premium support” -- to purchase health insurance. Under Ryan's plan, seniors would have the choice of buying private insurance or through Medicare’s traditional fee-for-service model.

The deficit
Tonight, President Barack Obama said his plan would cut the deficit by $4 trillion.

OBAMA: Now, we all know that we've got to do more. And so I've put forward a specific $4 trillion deficit-reduction plan. It's on a website. You can look at all the numbers, what cut we make and what revenue we raise.

That estimate comes from the left-leaning Center on Budget and Policy Priorities -- $3.8 trillion over 10 years.

The president is counting money saved by letting the Bush tax cuts expire for people making more than $250,000 a year.

But he's also counting on savings already agreed to last year when the White House and Congress agreed to raise the debt ceiling.

Taxes
At the outset of the debate, President Barack Obama and Republican presidential nominee Mitt Romney tangled over taxes. Romney objected to the president's claim that his tax cuts would cost $5 trillion.

ROMNEY: Let me repeat what I said, I'm not in favor of a $5 trillion tax cut. That's not my plan. My plan is not to put in place any tax cut that will add to the deficit.

What is Romney's plan?

He has proposed making the Bush tax cuts permanent for all income levels -- then cutting all rates by an additional 20 percent. He would also repeal the alternative minimum tax and permanently repeal the estate tax.

The non-partisan Tax Policy Center concluded that Romney's tax plan would cost $4.8 trillion over 10 years.

Romney said -- once again tonight -- that his plan would be paid for by closing loopholes in the tax code and by getting rid of some tax deductions and credits. But he has repeatedly declined to say which deductions he'd eliminate, saying he'd work with Congress to make those decisions.