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He said it makes more sense to furlough senior managers and those near retirement, while keeping lower-level workers — those who are doing the enforcement or services such as air traffic controllers — on the job.

“What’s amazing to me about all this is you’ve got the furloughs going on in the agencies and they don’t seem to be linked to anything other than an across-the-board strategy,” Mr. Light said.

About a quarter of the job openings posted by Monday evening were in medical or public health, 67 were in management or clerical services, and another 21 were in information technology.

The Defense Department led the way with 123 jobs posted as of Monday evening, while the Department of Veterans Affairs was close behind with 119 jobs.

The Justice Department, which has issued furlough notices to 115,000 employees, had a handful of job openings, including one to hire “several” law librarians, with annual salaries up to $115,742, and another posting for a student intern to answer phone calls and sort documents for up to $18.97 an hour.

There was one opening for a professor at the Army War College in Pennsylvania, at a salary of up to $115,811 a year. A War College spokeswoman said the professor’s post was deemed critical for their academic mission.

The lowest-paying jobs were working at swimming pools, golf courses and bowling alleys on Army bases. Each of those began at the federal minimum wage of $7.25 an hour.

An Army spokesman said those jobs are funded through fees paid to those facilities and don’t get taxpayer money.

But that explanation didn’t wash with some watchdogs.

“All money is fungible,” said John Hart, spokesman for Sen. Tom Coburn, Oklahoma Republican and Congress’s top waste-watcher. “Mobilizing our nation’s aircraft carriers seems to be a more pressing priority than mobilizing our nation’s taxpayer-funded bowling alleys. The administration’s refusal to set priorities continues to make a mockery of their doomsday predictions.”

Mr. Coburn last week called for the government to stop filling low-priority jobs, pointing out a number of openings such as a museum director and 10 new drivers for State Department cars.

The White House at first seemed cool to the idea, but then issued a memo urging offices to be careful about any hires they made. The White House budget office also warned against hiring outside contractors to try to make up for the lost work from federal employees.

The budget office didn’t return messages seeking comment Monday, nor did the U.S. Forest Service or the Army Corps of Engineers.

One decision agencies face is how to handle internships. A number of intern openings were posted Monday, with duties ranging from answering phones to taking part in intensive engineering programs.

The federal Office of Personnel Management said agencies are allowed to make all hiring decisions and furlough decisions and that includes hiring interns, which the office said “is still an important part of an agency meeting its mission.”