A federal budget compromise that was hailed as historic for proposing to cut about $38 billion would reduce federal spending by only $352 million this fiscal year, less than 1 percent of the bill’s advertised amount, according to the Congressional Budget Office.

Although that analysis dampened enthusiasm for the deal among many Republicans on Thursday, the House and the Senate approved the measure with bipartisan support. President Obama is expected to sign the bill Friday, officially ending the prospect of a government shutdown.

The findings from the budget office warned that the deal may never come close to delivering on its promises. The analysts found that $13 billion to $18 billion of the cuts involve money that existed only on paper and was unlikely to be tapped in the next decade.

The shrinking appearance of the reductions changed Thursday’s atmospherics on Capitol Hill. Just days after he was hailed for “winning” negotiations with the White House and Senate Democrats, House Speaker John A. Boehner (R-Ohio) was making a last-minute plea for votes from members of his party.

In the end, about one-quarter of House Republicans voted against the bill. That total included 28 of the 87 Republican freshmen, who had won election by promising that the solutions were simple — it was how Washington works that was unnecessarily complicated.

For some, the news of this accounting alchemy showed how complicated the place remains, even with them in it.

“It was a factor in what pushed me toward ‘no,’ ” said Rep. Joe Walsh (Ill.), one of 28 Republican freshmen who voted against the deal. “This is just the way that both parties have done business for a long time. And I just don’t want to be a part of that stuff.”

Boehner rejected the idea that the cuts were not as large as they appeared. Rather, he said, the impact could be much larger: In part because it would shrink the baseline budget left to future Congresses, it might save up to $315 billion over 10 years.

“There are some who claim that the spending cuts in this bill aren’t real, that they’re gimmicks,” Boehner said in a speech before the House’s vote. “Well, I just think it’s total nonsense. A cut is a cut.”

The problem — in the murky mathematics of the federal budget — is that not all “spending” is really spending.

Understanding why requires knowing that the government does not work like a savings bank. Agencies do not have their own checking accounts, fattened up
every year with new money from Congress.

Instead, Congress usually gives agencies the authority to draw from Uncle Sam’s one gigantic checking account. That is the Treasury’s General Fund, which is constantly taking in taxes, fees and borrowed money.

The agencies can’t take money out of this fund until they’re ready to spend it.

And that’s where it becomes complicated.

Sometimes, agencies aren’t ready to spend the money until a year, or longer, after Congress gives them their IOU. That’s not a problem when an agency makes a one-time purchase for something like pencils. Officials call a supplier, get their pencils and write a check, and the money is gone.

But it works differently when the government buys an aircraft carrier.

“The final check doesn’t go out until the carrier has gone through sea trials,” said Scott Lilly, a budget expert at the liberal Center for American Progress. “And that’s about six years later.”

The compromise bill has canceled some of these long-term IOUs. These are real cuts, experts say: They stop spending that was going to happen. But they aren’t counted in the current fiscal year, because the money was going to be spent later.

That’s part of the reason why just $352 million in the cuts will be felt during fiscal 2011. In fact, when “emergency” money for military action is factored in, the overall spending for this fiscal year may actually increase, by more than $3 billion.

Then there are the cases where IOUs were sitting idle and un-used.

This might be because a project was finished under budget, with some money left over. It might also be because a project was cancelled, or because an agency simply chose not to do something that Congress gave it money to do.

The result is leftover budget authority. Some expire at the end of the fiscal year. But others roll over, which can leave agencies with rainy-day funds filled with billions in theoretical money.

The compromise bill canceled some of these IOUs, too. But, experts say, these shouldn’t count like the others: It’s not exactly a cut if the money was never going to be spent.

“There was permission to spend money, but there were never actual dollars allocated,” said Brian Riedl of the conservative Heritage Foundation. “It’s kind of like a parent saying, ‘If you go buy something, I’ll pay the credit card for you.’ And then the kid never goes out and buys it.”

A Washington Post analysis of the 459-page budget revealed at least 98 cases in which Congress took back unused IOUs and called it a cut.

In some instances, federal agencies said they really were about to use the money. At U.S. Customs and Border Protection, for instance, a spokesman said the loss of a $10 million IOU would delay the replacement of aging equipment. The Census Bureau lost $50 million it was planning to spend on support personnel and things such as IT infrastructure.

But in other cases, the IOUs seemed unlikely to be cashed in.

The compromise budget, for instance, takes $560 million from the Academic Competitiveness and SMART programs, which gave grants to college undergraduates.

But the programs are set to end after this school year. And
the Education Department has enough cash to cover the remaining grants. “We would not have used this money,” a spokesman said.

At the Treasury Department, Congress gave itself credit for rescinding $423 million from a program that uses forfeited assets to aid criminal investigations.

But there, too, the cut was less impressive than it sounds. Last year was a banner year for forfeited assets: The fund took in $1.2 billion after a series of financial-crime cases and found it had far more money than it could use.

At the Department of Homeland Security, the Federal Air Marshal Service lost $2.4 million and the Coast Guard $13.5 million. But both already had enough money to cover expenses, a spokesman said. “There is no impact.”

Congress took back one IOU from . . . itself.

When the Capitol Visitor Center was under construction, lawmakers allotted $621 million to pay for it. The project wound up costing less than $600 million. In the compromise budget, lawmakers took back $15 million of the unused budget authority.

Spokesmen for both parties in Congress defended these moves this week, saying it was a good thing to take back authority that federal agencies might have eventually used.

“They prevent Washington bureaucrats from spending money,” said Michael Steel, a spokesman for Boehner.

“Is it a taxpayer dollar? Then it counts,” said Jon Summers, a spokesman for Senate Majority Leader Harry M. Reid (D-Nev.). He said that if the IOUs weren’t revoked, agencies could have found ways to spend the money — turning it from theoretical to real.

“I mean, is it better to just leave the money sitting there?” he said.

Staff writers Philip Rucker and Felicia Sonmez contributed to this report.