The sequester cuts are now officially in place, but many government agencies appear to be hiring freely anyway.

The U.S. Forest Service on Monday posted help-wanted ads for a few good men and women to work as “recreation aides” this summer, the Internal Revenue Service advertised for an office secretary in Maryland, the U.S. Mint wanted 24 people to help press coins, and the Agriculture Department said it needs three “insect production workers” to help grow bollworms in Phoenix.

Monday marked the first regular workday under sequestration, and federal agencies posted more than 400 job ads by 6 p.m.

At a time when nearly all of those agencies are contemplating furloughs, the help-wanted ads raised questions about how agencies should decide between saving through attrition or letting people go.

“Every position you don’t fill that isn’t absolutely necessary is one less person that needs to be furloughed,” said Steve Ellis, vice president at Taxpayers for Common Sense — though he said some positions that people leave need to be filled in order to meet agencies’ core missions.

Part of the problem is it’s often unclear exactly what those core missions are, said Paul C. Light, a professor at New York University who has studied government organization extensively.

“When you say mission critical, it’s a phrase without meaning,” he said. “Everything’s mission critical. Therefore, we have no way of knowing what would be mission critical in a job description versus what is not.”

He said agencies become “very artful” in writing job descriptions to justify why they are hiring.

At the Homeland Security Department, which just days ago announced it was releasing some low-priority illegal immigrants from jails to await removal, the agency in charge of deportations advertised for an assistant to help with deportations.

The annual salary for the job is $60,765, enough to detain one immigrant for about 500 days.

An official at U.S. Immigration and Customs Enforcement said the agency is filling only mission-critical positions and may not end up hiring for every job it advertises.

The sequesters — $85 billion in spending cuts — were set into motion by the 2011 debt deal and imposed across-the-board cuts to most federal agencies. Social Security was spared, and other big entitlements such as Medicare face only minor trims.

Homeland Security officials warned that they would have to furlough airport screeners, and the Defense Department has canceled deployment of a second aircraft carrier to the Persian Gulf region to save money.

But the Obama administration also faces a decision about how painful it wants the cuts to be. Ahead of the sequesters, when the White House was still hoping for a deal, officials painted the most dire picture possible. Now that the cuts are a reality, the administration must grapple with the possible downside of cutting something critical while spending on something that voters might see as less important.

When it comes to furloughs, Mr. Light, the NYU professor, said it would make sense to use job appraisals to decide which employees to furlough — except that the appraisals aren’t particularly useful anymore.

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.”

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