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The Obama administration's statement that the government will not be adding to the debt by the middle of the decade clashes hard against the facts, Republicans say, leaving officials straining to justify the budget claim they've pushed repeatedly over the past few days.

As it turns out, the administration is not counting interest payments. That means the budget team plans to have enough money to pay for ordinary spending programs by the middle of the decade. But it won't have the money to pay off those pesky -- rather, gargantuan -- interest payments. So it will have to borrow some more, in turn increasing the debt and increasing the size of future interest payments year after year.

So how then, visibly agitated Republicans asked, can the administration claim that its 2012 spending plan sets the country on a course to "pay for what we spend" in just a few years?

"We're still going further into debt, massively," Sen. John Ensign, R-Nev., told White House Budget Director Jack Lew at a budget hearing Tuesday, accusing the administration of "double-talk."

Anyone who gives the budget chart a cursory glance can see the debt will continue to skyrocket under the White House proposal. In fact, the long-term outlook shows the public debt -- which isn't even the entire debt -- soaring from about $11 trillion this year to nearly $19 trillion in 2021. Driving that increase is the fact that annual deficits will never fall below $600 billion.

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To justify the administration claim, Lew said the administration was merely referring to "primary balance" -- or federal spending minus interest payments. Lew sought to forgive the public for their confusion.

"The terminology that we use in Washington of primary balance is a little confusing," Lew said.

"It's because I believe it's dishonest," Ensign shot back.

Republicans were understandably befuddled. To put the scenario in everyday terms, it's like a family claiming that they've balanced the family finances, but neglecting to mention that they're taking out a new loan every month to pay off credit-card interest. As a result, the family keeps going deeper into debt.

For an $80 interest payment, that might be manageable. But this is the United States budget. If the government does what the Obama administration is recommending, net interest payments will go from about $200 billion this year to $844 billion in a decade. That's more than the country spends now on Social Security.

White House Press Secretary Jay Carney, at his first official press briefing on the job, used the credit card analogy Wednesday and acknowledged interest rates "have to be contended with."

"But the first important step in dealing with this issue is getting your regular spending and income in balance so that you're no longer adding to the problem," he said. "And interest payments are a major portion of our long term debt problem that we need to address. But it is not an inconsequential deal."

Yet President Obama and Lew neglected to explain this point in their initial statements. Lew, in an interview Sunday on CNN's "State of the Union," said: "Our budget will get us, over the next several years, to the point where we can look the American people in the eye and say we're not adding to the debt anymore. We're spending money that we have each year, and then we can work on bringing down our national debt."

Obama, discussing his budget in Baltimore Monday, said the proposal "puts us on a path to pay for what we spend by the middle of the decade."

In his press conference the next day, Obama went further.

"What my budget does is to put forward some tough choices, some significant spending cuts, so that by the middle of this decade our annual spending will match our annual revenues. We will not be adding more to the national debt," he said.

Pressed to explain this claim, the president hinted at the rationale.

"We've racked up a whole bunch of debt. And there's a lot of interest on that debt," he said. "So in the same way that if you've got a credit card and you've got a big balance, you may not be adding to principal. You've still got all that interest that you've got to pay. Well, we've got a big problem in terms of accumulated interest that we're paying and that's why we're going to have to whittle down further the debt that's already been accumulated."

Under questioning from Senate Republicans Tuesday, Lew acknowledged the government would be adding to the debt by borrowing to pay interest, but still stood by his statements.

"We're getting further in debt ... because of our interest rate," Ensign said.

"Yeah," Lew responded.

Sen. Jeff Sessions, R-Ala., ranking Republican on the Senate Budget Committee, grilled Lew over this disconnect.

"We are adding to the balance, and we're not cutting up the credit card. That's just the fact," Sessions said, calling the administration's claims "misleading."

Lew stood by his claim. "What I said was we're going to stop adding to the debt. Our spending will not add to the debt," he said. "It's an accurate statement."

Sessions disagreed, calling the assessment "not a legitimate way to analyze it."

The website PolitiFact, which tries to sort out politicians' policy claims, analyzed the administration's argument in an article Tuesday and gave it a rating of "false."

The White House later claimed that the debt would not increase as a share of the economy -- that's technically true, given that the public debt would level out at about 76 percent of GDP by mid-decade. But that assumes a certain level of growth in the economy and also assumes the debt, as a figure, will continue to rise year after year. PolitiFact ruled that its "false" rating would remain unchanged, given that Obama did not make that distinction in his press conference.