A sign indicating that the National Archives Building is closed because of the federal government shutdown Monday. (Andrew Harrer/Bloomberg News)

Hundreds of thousands of federal employees in the Washington region began their workweek on a gray-sky Monday facing a brief, unnerving government shutdown that left many fearing what lies ahead.

Workers throughout the nation’s capital were packing up their desks, collecting their furlough letters and leaving their offices when word came shortly after noon that the Senate had reached an agreement to reopen — until Feb. 8.

“Oh, good. We’ll get to do all this over again in three weeks?” asked a Justice Department staffer who, as he walked up Pennsylvania Avenue, spoke on the condition of anonymity so he could more freely criticize elected leaders for once again failing to make a long-term deal.

“How do I know what they’ll do?” he said. “They clearly don’t have a clue themselves.”

Errick King, a federal employee for 30 years, thinks he knows exactly what lawmakers will do next: more of the same.

The Constitution gives Congress power over the D.C. budget. This is what residents can expect when the federal government shuts down over spending battles. (Claritza Jimenez/The Washington Post)

Congress has not balanced a budget in years, and King doesn’t expect them to come February. That has left the father of three feeling so hopeless that he has considered changing his family’s lifestyle, including skipping the after-church meals out on Sunday afternoons and nixing the weekly bowling games they so enjoy.

The relentless instability, he said, is leading career employees to retire early and abandon agencies, leaving them increasingly thin on institutional knowledge.

“People are fed up,” said King, an IT specialist with the Bureau of the Fiscal Service in Hyattsville, Md. “I think it hurts the government overall because you are losing that knowledge and skill. We are reliant on that to provide quality service.”

The Washington region is home to the country’s largest concentration of federal employees and contractors, with 367,000 who work for the government and 450,000 who depend on federal contracts, said Stephen S. Fuller, an economist at George Mason University. He said about a quarter of the area’s economy depends on federal payroll or procurement spending.

John Rigg, who started at the Department of Health and Human Services in 2010, is among those employees whose tolerance for Capitol Hill mismanagement has all but evaporated.

He’s had a number of private-sector opportunities in recent years and is wondering if he should finally pursue one of them.

“The thing the 2013 shutdown emphasized was that I need to assume more risk in federal employment,” Rigg said. “My wife and I have increased the savings we set aside to cope with that risk. It makes me less inclined to think about federal employment in the long run.”

In the hours before the Senate came to its tenuous resolution, uncertainty over how long the shutdown would last had left people throughout the area both angry and anxious.

“It is a huge pain in the ass,” said a researcher on his way into the National Institutes of Health on Monday morning. The man, who declined to give his name, had come in to stop a stem-cell experiment designed to determine the cause of a disease that affects facial bones.

He worried about the effect on the NIH Clinical Center, where many people are treated with last-ditch experimental therapies.

“Nobody can be recruited to clinical trials” during a shutdown, he said. “We’re talking about cancers and pediatric cancers. So now we’re talking about children who won’t get treatment if it goes on.”

In Foggy Bottom, the sidewalks outside the State Department building were packed with employees walking in both directions. The furloughed workers, many with a look of grim resignation on their faces, left carrying sheets of paper outlining the furlough rules.

“I’m going to go home and go back to sleep,” said one Foreign Service officer who declined to provide her name or the bureau where she works.

She had arrived at 8:30 a.m. and spent two hours fulfilling the orderly shutdown protocol before heading out. Some of her furloughed co-workers, she said, spent part of the morning trying to sneak in a last bit of work.

“Everyone’s itching to work,” she said. “It shows how dedicated everyone is. Some people got on their computers, and colleagues said: ‘Stop it. You’re not allowed to work.’ ”

Opinions varied on who was to blame for the shutdown, which began Saturday.

“It depends on your political leanings,” she said. “It’s something that surely could have been averted.”

For Margaret McDaniel, this was her third, and shortest, shutdown.

“What, they couldn’t have done that on Friday?” said the 27-year Agriculture Department staffer after the Senate announced its deal. “It blows my mind, it’s so damned irresponsible.”

This shutdown, though, was easier to prepare for than the previous two. McDaniel, a senior adviser in the Foreign Agricultural Service, is more financially stable than she was in 1996 or 2013, but she still worries about her more-junior colleagues. Even though she appreciates that the string of continuing resolutions keeps full funding in place when a ­long-term budget may bring program cuts, McDaniel laments the disruption of governing by standoff.

Darlene Davis, who lives in Hampton, Va., spent three hours commuting to and from work in Norfolk on Monday morning simply to sign her furlough letter. It marked the second time she’d endured the stress of a shutdown during her 17-year career as a civilian working for the Navy.

“Today was a complete waste,” said Davis, an education specialist. “To drive all the way out there and drive back, it’s frustrating beyond belief.”

Davis spent the weekend monitoring her spending in an effort to “conserve every ounce” of her income. She, too, fears being in this position again next month, a feeling that will leave her and other workers stressed about what’s to come as the provisional compromise expires.

“That’s just putting a Band-Aid on a pipe that’s about to burst,” she said. “My confidence in their ability to come to some sort of resolution in three weeks is at zero.”

She spent part of the day off updating her résumé and searching for jobs outside the government. At 53, Davis said, she needs a job that has financial stability.

“Everything about my life is up in the air,” Davis said. “It’s not fair to me, and the people like me to be in this place of uncertainty and unknowing about my job and about my finances. Who wants to live like that?”

Allyson Chiu, Michael E. Miller, Carol Morello, Shira Stein, Amy Goldstein and Lenny Bernstein contributed to this report.