Republican presidential candidate Ben Carson speaks to reporters before a GOP debate at the Ronald Reagan Presidential Library on Sept. 16 in Simi Valley, Calif. (Sandy Huffaker/Getty Images)

Ben Carson's interview with public radio's Kai Ryssdal didn't go very well.

The interview, for the program Marketplace, centered around the Republican presidential candidate's plans for the nation's economy and his views on the federal budget. During the conversation, Carson stumbled over a response about the debt limit and offered only vague indications of how he'd keep government spending in check.

Given that this is a complicated topic, we decided to break out Carson's responses to explain and evaluate them. (We've edited down the questions and answers, which can be read in their entirety at Marketplace's Web site.)

Ryssdal: [I]f we're gonna have a balanced budget amendment, government's gonna have to spend less, we're gonna have to get more money. What will you not provide in the way of government services? …
Carson: If we simply refuse to extend the budget by one penny for three to four years, you got a balanced budget. Just like that.

Carson's point is that spending and revenue tend to increase in concert. Data from the White House Office of Management and Budget showing federal receipts (mostly tax income) and spending illustrates how Carson's point would work.

(A quick reminder: The gap between revenue and outlays generates either a budget surplus -- when we take in more than we spend -- or a deficit. The federal debt is largely the accumulation of years of deficits.)

The OMB estimates that the government will take in $3.2 trillion in 2015. That would have been more than enough to fund the government if spending matched 2008 levels. (Except that this was in 2008 dollars, a not-insignificant distinction, but you get the point.) According to OMB estimates, we'll have about enough revenue in 2017 to fund the outlays we're making in 2015. So freeze spending at 2015 levels, and we've got a balanced budget in two years.

It's not that easy, of course. A certain number of spending costs necessarily rise over time, in part because of the changing value of the dollar and in part because the population is growing. Spending on Medicare and Social Security, for example, keeps going up.

Capping spending at 2008 levels, for example, means that Medicare would be able to pay only 72 percent of its projected 2015 bills — which means cutting benefits for recipients.

Back to Carson.

Carson: Having said that, one of the bugaboos that has kept us from reducing government in the past is sacred cows. … Take every departmental head, or sub-department head and tell them, "I want a 3 to 4 percent reduction." Now anybody who tells me there's not 3 to 4 percent fat in virtually everything that we do is fibbing to themselves.

The extent to which there is excess in every federal budget is a subjective question. But it's worth noting that reducing the budget by 3 to 4 percent across the board wouldn't actually eliminate the deficit. Dropping how much the country is projected to spend in 2015 gets us to $3.6 trillion in outlays. We're expected to have $3.2 trillion in revenue.

Ryssdal and Carson debate the deficit for a bit, and then Ryssdal turns to the debt limit.

Ryssdal: All right, so let's talk about debt then and the budget. As you know, Treasury Secretary Lew has come out in the last couple of days and said, "We're gonna run out of money, we're gonna run out of borrowing authority, on the 5th of November." Should the Congress then and the president not raise the debt limit? Should we default on our debt?
Carson: Let me put it this way: If I were the president, I would not sign an increased budget. Absolutely would not do it. They would have to find a place to cut.
Ryssdal: To be clear, it's increasing the debt limit, not the budget, but I want to make sure I understand you. You'd let the United States default rather than raise the debt limit.
Carson: No, I would provide the kind of leadership that says, "Get on the stick, guys, and stop messing around, and cut where you need to cut, because we're not raising any spending limits, period."

The distinction here is between the debt limit, which Ryssdal is asking about, and the debt.

A good (if simple) analogy for understanding the debt limit is that it deals with the ability to pay a credit card bill, not with how much you buy with your credit card. Carson's answer — and further answers as Ryssdal presses the point — deal with how he as president would keep the government from running up new debt. In other words, how he'd keep the country from running up its credit card in the first place.

The debt limit — also called the debt ceiling — is a cap on how much money can be borrowed to pay existing debts. "The debt limit does not authorize new spending commitments," the Treasury Department explains. "It simply allows the government to finance existing legal obligations that Congresses and presidents of both parties have made in the past." Carson is being asked if the government should do what it needs to in order to pay the credit card bill — and Carson doesn't really answer.

Reducing the debt would decrease the amount of money that is needed to pay on our debts — but whoever the next president is probably will still need to increase the debt limit to pay for what already exists. Having less debt, we'll note, also would reduce government spending. So far this year, we've spent $402 billion in interest on outstanding debt.

Carson reinforces his concerns about spending a bit later in the interview.

Carson: [W]e have a number of different areas that are contributing to the increasing expenditures and the continued expenditures that are putting us further and further into the hole. You're familiar I'm sure with the concept of the fiscal gap. … [T]he fiscal gap is all of the unfunded liabilities that the government owes. Medicare, Medicaid, Social Security, all the departmental programs, all the agency and sub-agency programs extending into the future, which is a lot of money, versus the amount of revenue that we expect to collect from taxes and other revenue sources.

Carson then pegs the size of the "fiscal gap" at $200 trillion.

The concept, in short, is that we've already made decisions that commit us to future spending. If you project the difference between those commitments and our projected revenue, you get a figure that's different than the number for the federal debt — which is only a tally of the debt that exists. The fiscal gap is the debt that we can expect to exist, based on our current path.

Because this deals with future projections, the size of the gap varies in different estimates. Carson probably was pointing to a 2011 study from Boston University's Laurence Kotlikoff that put the gap figure at $211 trillion. A lot of that expected cost came from the aging of the population and the costs of paying Social Security to retirees.

Over the course of the interview, Carson made his concern clear: He's worried about the debt. The extent to which he answered questions about how he'd deal with the debt is much murkier.