Before the House voted 260 to 167 to pass the 2011 budget agreement on Thursday afternoon, Republican leaders called in a GOP budget expert to brief rank-and-file members on the nitty-gritty of the deal.

The call to Douglas Holtz-Eakin came after a Wednesday report by the nonpartisan Congressional Budget Office created confusion over the scope of spending cuts agreed to last week by the White House and congressional leaders.

Holtz-Eakin, a former CBO director and economic adviser to Sen. John McCain’s (R-Ariz.) 2008 presidential bid, met with Republican House members at 11:30 a.m. Thursday in the Capitol Visitor Center to run through the intricacies of the budget deal. He also held a conference call for bloggers at 2 p.m., shortly before the House vote.

On the conference call, Holtz-Eakin declined to go into detail on the meeting with the lawmakers.

“My intent there was the same as my intent here, which is to educate them on the budget process, and I had the opportunity to do that, so I was pleased,” Holtz-Eakin said.

The report issued by the CBO indicated that the budget deal would trim only $352 million in expected spending for the current fiscal year, not the more than $38 billion projected by congressional leaders and the White House.

The confusion stems from the difference between budget authority and outlays. Budget authority is the permission that federal agencies have to spend money; outlays refer to the amount actually spent in a given fiscal year. Much of the cuts in agencies’ budget authority included in last week’s spending deal would affect spending for future years, not the 2011 fiscal year.

On Wednesday evening, House Speaker John Boehner’s (R-Ohio) office released a blog post arguing that the CBO report confirms the budget deal “will immediately reduce budget authority by nearly $40 billion versus fiscal year 2010” and provide an estimated $315 billion in deficit savings over the next decade.

“The federal budget is fiendishly complex, which makes it easy for people to misuse and misrepresent numbers,” a House Republican leadership aide said Thursday.

Later in the day, 179 House Republicans voted “aye” on the spending bill, apparently unconcerned about the CBO report.