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A spokesman later explained that committee members were frustrated that the initial estimate wasn’t labeled preliminary.

As CBO looks for new staffers, Mrs. Wasserman Schultz instructed Mr. Elmendorf to try to hire more women and minorities.

Mr. Elmendorf said they’ve tried, including recruiting at historically black colleges and universities, but said there aren’t many U.S.-citizen women and minorities earning doctoral degrees in economics, which means the hiring pool is small.

Mrs. Wasserman Schultz told him he needs to start a program to get to children well before college, because by that age women and minorities have already decided against math and economics.

“You’ve got to reach down much further,” she said, and directed CBO to take “a leadership role” in trying to raise awareness of math and economics as careers for women and minorities.

Further complicating CBO’s staffing problems is a new rule that prohibits him from hiring foreign nationals, who make up about half of all economics Ph.D.s, Mr. Elmendorf said. He said the week that rule passed last year, it had to abruptly cancel interviews with four applicants who weren’t U.S. citizens.

Both agencies strive to be scrupulously nonpartisan, which often means balancing the competing pressures from politicians, especially since both get so many requests for work they have to pick and choose.

Mr. Elmendorf said he has a chart divided into columns for House Republicans, House Democrats, Senate Republicans and Senate Democrats and lists the work he’s doing at the request of each, so they can make sure no chamber or party is getting more work done for it than the others.