McDonald is among a cadre of public servants with the skills employers crave in this historically tight labor market, and new job-search data shows that recruiters are reaching out to those workers during the shutdown. At the same time, federal employees are increasingly hunting for new roles, the figures reveal.

Official departure numbers are unknown for now as the shutdown continues, and authorities say it won’t be possible to tally the exodus until after work returns to normal at federal agencies. But as government employees meet with recruiters and ponder leaving jobs they’ve cherished, a new problem is emerging amid the nation’s longest-ever funding stalemate: the potential exodus of highly skilled workers.

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Labor groups say that such a loss of talent could weaken the federal workforce for years, draining institutional memory, countless hours of training and a shared sense of mission.

“This extended, painful shutdown is undoubtedly going to create a brain drain in the government,” said Lee Stone, western federal area vice president of the International Federation of Professional and Technical Engineers, which represents employees at NASA and other agencies. “We will be losing our best people, and we will not be able to get them back.”

Beyond the shutdown’s shrunken budgets, furlough boredom, snaking airport security lines and concerns about late tax refunds, the labor shift could hurt the government’s ability to recruit. College graduates don’t want to sign up for work that could leave them unpaid for a month or more, Stone said, and employees with decades of experience are opting to retire early without getting the chance to pass down their knowledge.

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As paychecks froze for thousands of federal workers — and evaporated for contractors who are not guaranteed back pay — recruiters seemed to spot an opportunity, according to new LinkedIn data provided to The Washington Post.

Inquiries to employees at temporarily shuttered agencies surged by 60 percent in January compared with the same month last year, the job-networking platform found Thursday, “indicating that companies are targeting these workers for new roles.”

The most sought-after profiles tended to feature specialized skills, researchers found: Software engineers, attorneys and program managers. (TSA workers also experienced a boost in interest.)

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“A lot of federal workers are people with college degrees that the private sector wants to tap,” said LinkedIn chief economist Guy Berger. “And six, 12, even 18 months from now, we’re going to see if the average level of talent in government has struggled to rebound from this shutdown.”

In Kansas City, Mariam Hicks, 36, an IRS manager, said she has started opening messages from headhunters on LinkedIn.

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“I was wondering if you’d be interested in learning more about this opportunity,” one bank recruiter asked her on Dec. 17, days before the shutdown began.

She ignored it.

By Jan. 9, her thinking changed. The government remained stubbornly closed. Her savings account hit $700.

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She wrote back.

“I’d love to hear more about this.”

The following week, she took a temporary job at a sports clothing store to earn cash while furloughed.

As recruiters target them, more federal workers are exploring other possibilities on their own, according to new data from Indeed, an employment website with 250 million unique monthly visitors.

Since Dec. 1, job searches among IRS employees have spiked by 50 percent, the numbers show. Indeed inquiries leaped by 30 percent from TSA workers, 40 percent from staffers at the Department of Homeland Security and 56 percent from those at the Defense Department.

“The jumps in search activity at agencies where workers aren’t getting paid are dramatic,” said Martha Gimbel, research director for the Hiring Lab at Indeed.

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These days, even the federal workers who are getting paid appear to be eyeing the exits, she said: “The question is: Are federal workers starting to rethink government employment altogether?”

For some, the draw of a generous federal pension has long made up for pay disparities between the public and private sectors. But now, that wage gap and missing pay have heightened the temptation to flee. Federal worker salaries trail those of similar private-sector employees by nearly a third on average, according to the Federal Salary Council. The gap is widest in the San Francisco area, followed by greater Washington, D.C., and Baltimore.

Government engineers, researchers, biologists and lawyers — “they have the best pick from the available jobs out there,” said Stone, a NASA scientist. “And once they taste that pay increase, they wonder, ‘Is it worth it?’ ”

McDonald, 56, who lives in Laurel, Md., and has spent 30 years working for the government — most recently at FEMA — said the government has paid to train her in negotiations, managing federal property, drafting cost assessments and inking hundred-million-dollar deals.

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“That’s cost them a small fortune,” McDonald said.

She wanted to pay it forward. Help her fellow Americans. The job felt more like a calling, and she had never seriously thought about ditching it.

But more than a month without income has spooked her into considering the private sector. She’s already checked out prospects in Louisiana, where her family resides. The next move?

“Any company that buys things or has contracts,” she said.

McDonald doesn’t place the blame on either political party, but she says it’s imperative that the government shutdown ends. “It’s going to cause long-term damage.”

The federal employees who are watching from the sidelines or working without pay are supposed to be creating the future of space travel, inspecting the food we eat, testing rivers for toxic chemicals, checking up on hurricane-torn communities.

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“These are professional-grade workers,” said Marlo Bryant-Cunningham, chief steward at a union that represents workers at the Office of Personnel Management. “They have degrees. And they’re at their wit’s end.”

Matt Linton, 38, quit his job at NASA during the 16-day government shutdown in 2013, doubling his salary by taking a job at a private technology firm, where he is focused on thwarting hackers.

“I am receiving résumés from current NASA employees who are realizing I made the right call in 2013,” he said. “They’re asking me: Can you get us in somewhere?”

Silvano Colombano, 73, a scientist at NASA’s Ames Research Center in Mountain View, Calif., said the shutdown is pushing him toward a milestone he’d been putting off: leaving government service.

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“I wasn’t planning on doing that, but I’m frankly so angry at this point — about being used as a pawn — that I’d rather work in the medical industry,” he said, noting that he would regret losing out on the chance to coach younger colleagues, the future of the agency. “But if the government treats you like this, why bother?”

At FEMA, six workers have quit since the government hit pause, said Steve Reaves, president of the American Federation of Government Employees Local 4060.

“A lot of employees have said, ‘Hey, I’m floating my résumé,’ ” he said.

As for him?