The presidential candidates disagreed a lot in Wednesday night's debate. But they also said several times that they agreed. They agree, for example, that the federal budget deficit is a major problem. It started growing in the early 2000, exploded during and after the financial crisis, and has dropped a little but remains immense. The two men fundamentally disagree about what to do now.

As part of Solve This, our series on major challenges facing the country, NPR's David Welna examines the competing approaches of Mitt Romney and President Obama.

DAVID WELNA, BYLINE: The gap between what the government takes in and what it shells out has exceeded $1 trillion every year of Barack Obama's presidency. And yet contrary to what many had once predicted, that shortfall so far has not pushed up interest rates or triggered runaway inflation, which may be why Mitt Romney warned at the Denver debate of the perils of deficit spending not so much as an economic hazard but as a moral one.


MITT ROMNEY: I think it's frankly not moral for my generation to keep spending massively more than we take in, knowing those burdens are going to be passed on to the next generation.

WELNA: Pressed on the deficit last month on late night TV, President Obama made clear to David Letterman that it could become a problem, but it's not one right now.


PRESIDENT BARACK OBAMA: We don't have to worry about it short term. Right now interest rates are low because people still consider the United States the safest and greatest country on Earth, rightfully so. But it is a problem long term, and even medium term.

WELNA: Which may be another way of saying something should be done, though not quite yet. The president ought to be wary of slashing government spending before the economy has truly recovered, says Paul Van de Water of the Center on Budget and Policy Priorities, a liberal Washington think tank.

PAUL VAN DE WATER: In the near term, obviously, the economy is still very weak, and there's great concern that attempting to reduce the deficit too quickly could actually throw the economy back into a recession.

WELNA: Still, unlike Romney, President Obama has laid out a plan to reduce projected spending over the next decade by $4 trillion. Not enough to balance the budget, but enough, he said at the Denver debate, to stabilize the size of the federal debt as a portion of the overall economy.


OBAMA: The way we do it is $2.50 for every cut, we ask for a dollar of additional revenue, paid for, as I indicated earlier, by asking those of us who have done very well in this country to contribute a little bit more to reduce the deficit.

WELNA: But a trillion dollars of the president's proposed cuts would come from ending the wars in Iraq and Afghanistan, something he planned to do anyway. And while letting the top Bush-era tax cuts expire could boost revenues by a trillion dollars, there's still a shortfall, says Robert Bixby, head of the Concord Coalition, a budget watchdog group.

ROBERT BIXBY: Sometimes one is left with the impression in the Obama campaign that all we need to do is let the taxes go up for wealthy people and that would solve a major part of our problem. In fact, I think we're going to have to do a lot more and concentrate on the spending side.

WELNA: Mitt Romney avoided talking numbers in Denver.


ROMNEY: I will eliminate all programs by this test, if they don't pass it. Is the program so critical it's worth borrowing money from China to pay for it? And if not, I'll get rid of it. Obamacare's on my list. I apologize, Mr. President.

WELNA: But according to the Congressional Budget Office, eliminating Obamacare would actually add more than $100 billion to the debt over the next decade. Romney would actually increase defense spending and target domestic spending for cuts. That won't work, says the Concord Coalition's Bixby.

BIXBY: If we're going to get serious about bringing the debt under control, we have to take serious measures, and focusing on the non-defense discretionary side of the budget is probably the least serious type of measure we can take.

WELNA: And while Romney argues economic growth will boost revenues, even though he cuts income taxes by 20 percent, former Reagan administration official Bruce Bartlett says history would prove Romney wrong.

BRUCE BARTLETT: And Ronald Reagan recognized that his tax cut ultimately reduced federal revenues by supporting 11 major tax increases while he was president.

WELNA: Something Romney, unlike President Obama, vows he'll never do. David Welna, NPR News, the Capitol.

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