GOP presidential nominee Mitt Romney and President Barack Obama square off in the first presidential debate.

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.

NBC's Andrea Mitchell does a bit of fact checking after President Barack Obama and GOP nominee Mitt Romney faced off in the first 2012 presidential debate.

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.

President Obama and GOP presidential nominee Mitt Romney debate how to approach reducing the national deficit.

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.

GOP presidential candidate Mitt Romney steps out of turn to point out errors he feels President Barack Obama made in describing his tax plan.

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.