President Obama will meet with congressional leaders today in another attempt to avert the fiscal cliff — the automatic tax increases and spending cuts set to take effect Jan. 1 unless Congress can strike a deal. The cuts and tax hikes, which total more than $500 billion, are so large and so sudden that many economists fear they would plunge the country back into recession.

As Washington tries to hash out a deal, we've taken a step back to break down the numbers behind our deficit — how it grew so big, why it is actually shrinking and whether a deal can bring it under control.

How much are we in debt?

The federal debt is just shy of $16.4 trillion at the moment, which also happens to be the debt limit that Congress set in 2011. Treasury Secretary Timothy F. Geithner announced on Wednesday that the nation would hit the limit on Dec. 31. The Treasury can take some "extraordinary measures" to keep paying its bills for a few weeks, but it'll run out of cash by February or March unless Congress raises the limit again.

And that's different from the deficit, right?

Yes. The debt is the total amount of the government's outstanding obligations. The deficit is how much the government is in the red in a given year. In the 2012 fiscal year, which ended Sept. 30, the deficit amounted to $1.1 trillion.

That seems like a huge number. How did the deficit get so big?

The 2012 deficit was actually the smallest one since 2008. But it's still a giant shortfall.

As Binyamin Appelbaum noted in The New York Times, the federal government has run a deficit in 45 of the last 50 years. (The exceptions were 1969 and 1998 through 2001.) The financial crisis in 2008, however, caused the deficit to skyrocket, as tax revenues fell because of the slump in incomes and production, and government spending on the stimulus and safety net measures such as unemployment insurance shot up. The deficit for the 2008 fiscal year was $455 billion. In 2009, it surged to more than $1.4 trillion.

Since then, the deficit has been falling, albeit very slowly. The government took in 6.4 percent more in taxes in 2012 than in 2011, as the economy improved a bit and several tax breaks expired. And it spent less on Medicaid, unemployment insurance and the continuing operations in Iraq and Afghanistan.

What about the total debt? How much of that is President Obama's fault?

The debt has grown by nearly $6 trillion since Obama took office, from $10.5 trillion to $16.4 trillion.

Figuring out how much of that is due to Obama is tougher. The Washington Post's Ezra Klein, working with the Center on Budget and Policy Priorities, calculated in January that the legislation Obama had actually signed — as opposed to factors like the economy — had added about $983 billion to the debt.

Klein has also rounded up several charts that break down exactly what's caused our debt to grow so large. The biggest single factor has been the weak economy; President George W. Bush's tax cuts and the wars in Iraq and Afghanistan also fueled the debt buildup, as did President Obama's stimulus.

Have debt levels ever been this high before?

Yes, proportionally. Economists like to talk about a country's debt in relation to its gross domestic product (a measure of the economy's total annual output). And instead of using a country's total outstanding debt to calculate this debt-to-GDP ratio, economists typically use the amount of debt held by the public. (Somewhat confusingly, the federal government holds about $5 trillion in obligations to itself, most of which is money owed to the funds that support Social Security and other programs.)

Using this measurement, our debt was about 67.7 percent of GDP last year. As this chart compiled by Quartz's Ritchie King shows, that's the highest our debt-to-GDP ratio has been since the 1940s, when the need to finance World War II caused the debt to surge to 112.7 percent of GDP. But the economy grew fast enough after the war that the debt soon became a much smaller percentage of the country's GDP.

It's worth noting that a number of other developed countries have higher debt-to-GDP ratios than the U.S. Germany's public debt is 80.6 percent of GDP, and Canada's is 87.4 percent. The euro zone's most troubled countries fare even worse: Italy's debt is 120.1 percent of GDP; Greece's is 165.3 percent.

At least we're not Greece. How much longer can we keep borrowing?

That's a tough one. Some commentators — including Paul Krugman, the Nobel-winning economist and columnist for The New York Times — have argued that our current deficits are mostly a product of the sluggish economy. The deficit, Krugman wrote last week, "is a side-effect of an economic depression, and the first order of business should be to end that depression — which means, among other things, leaving the deficit alone for now."

Other economists — including Carmen Reinhart and Kenneth Rogoff, who studied eight centuries' worth of financial crises for their book "This Time Is Different" — argue that countries with debt-to-GDP ratios above a certain level tend to experience slower economic growth. Reinhart and Rogoff suggest the level is around 90 percent of GDP — which the U.S. is rapidly approaching. A recent Congressional Research Service report concluded that while the debt-to-GDP ratio can't keep rising forever, "it can rise for a time." The report continued:

It is hard to predict at what point bond holders would deem it to be unsustainable. A few other advanced economies have debt-to-GDP ratios higher than that of the United States. Some of those countries in Europe have recently seen their financing costs rise to the point that they are unable to finance their deficits solely through private markets. But Japan has the highest debt-to-GDP ratio of any advanced economy, and it has continued to be able to finance its debt at extremely low costs.

How does all this fit into the fiscal cliff? Would a deal to avert it fix our debt problem?

Actually, going over the fiscal cliff would almost singlehandedly erase the deficit. Tax rates would shoot up, and the fiscal cliff's indiscriminate budget cuts would slash military and safety-net spending alike.

The problem is that all those tax increases and spending cuts would likely throw the economy back into a recession, causing the deficit to balloon again. "The economy will, I think, go off a cliff," said Ben Bernanke, the Federal Reserve chairman.

(For more detail, see The Washington Post's exhaustive fiscal cliff explainer.)

What the two sides are trying to do is identify cuts that are ultimately deep enough to bring down the deficit — and thus, eventually, the debt — without stalling the economy. But negotiations collapsed last week after John Boehner, the Republican House speaker, tried and failed to pass a "Plan B" alternative to the president's proposal in the House. Obama is set to meet with congressional leaders today to try to strike a deal to block at least some of the cliff's impact by Monday night. But its prospects seem dim.

"I have to be very honest," Sen. Harry Reid, the majority leader, said on Thursday. "I don't know timewise how it can happen now."

Of course, some analysts have pointed out that people on both the Republican and the Democratic sides may actually want to move the cliff just slightly down the road into the next Congress, which convenes Thursday, Jan. 3. The advantages: Boehner can be safely re-elected as Speaker before he has to do serious twisting of arms of fellow GOP House members to get their votes for any compromise plan. And there will be a few more Democrats in the House and the Senate for the White House to rely on in enlisting the votes it needs to ratify any such deal. The disadvantage: Delay makes the risk of miscalculation greater for either or both sides — and for the public.