Federal employees have been skeptical for months that the biggest cuts to government spending in history could really happen. But with the “fiscal cliff” a week away, workers are now growing increasingly alarmed that their jobs and their missions could be on the line.

President Obama and members of Congress headed out of town late last week for a Christmas break without reaching a deal to avoid $110 billion in automatic across-the-board spending cuts, which would hamstring operations ranging from weather forecasting and air traffic control to the purchase of spare parts for weapons systems. So civil servants are bracing for the blow, wondering whether their work will be upended — and whether they may be forced to take unpaid days off.

“This could change day by day,” said Antonio Webb, 25, who works in the mail service that handles correspondence for the Department of Homeland Security. “You could come into work and the next day they say, ‘We don’t need you because we have to cut so much.’ ”

Many federal workers have become jaded after a two-year pay freeze and congressional fights over spending that keep agencies lurching from one stopgap budget to another. Until recently, few employees thought it could come to this: Budget cuts of 8 to 10 percent divided equally between military and domestic agencies. Only a few programs, like Social Security, veterans benefits and some services for the poor, are exempted.

“Sure, we continue to do our jobs,” said Carl Eichenwald, who works in enforcement at the Environmental Protection Agency. “But all of this uncertainty is disruptive for our mission. A lot of time gets spent spinning wheels. We won’t know whether we can do inspections. Do we have 100 percent of our budget, or 85 percent?”

What going over the 'fiscal cliff' would mean . . .

Top congressional aides said Monday that discussions of how to avert the fiscal cliff had come to a virtual standstill. Obama and House Speaker John A. Boehner (R-Ohio) had not spoken since Friday.

Each side in the negotiations urged the other to come up with a way around the impasse. A senior Democratic aide said Boehner needs to return from the holiday with a “cleared head and a readiness to deal.” The aide said that there is no time for Democrats to unilaterally advance a bill in the Senate, adding that they can press forward with legislation only if they are assured by Republican leaders of GOP support.

A senior Senate Republican aide insisted, however, that it is now up to Senate Majority Leader Harry M. Reid (Nev.) and his fellow Democrats to figure out what they can pass in the Senate without worrying about the Republican-controlled House.

As the year-end deadline approaches, federal employees have been told very little by their bosses about how their agencies are preparing to carry out huge spending reductions.

“It seemed like we were almost immune to thinking that something real was going to come of it,” said Fernando Cutz, an analyst for the U.S. Agency for International Development.

Then came an e-mailed memo on Thursday from agency heads to employees. The cuts would be “significant and harmful to our collective mission.” Furloughs “or other personnel actions” — layoffs — remain a real possibility.

Comptroller General Eugene Dodaro, in a lengthy video message, for instance, told employees of the Government Accountability Office that the agency would absorb a $42 million cut this year through a hiring freeze, slashed bonuses, eliminated technology projects and restricted travel. But those cuts “will not get us all the way there,” he said, and he did not mince words. “Some number of agency-wide furlough days” would be necessary.

The memos were also meant to make clear that the government would be open for business the day after New Year’s even if Obama and Congress fail to reach a deal to avoid the spending cuts.

“We wanted to make sure there was no confusion before people left for the holidays that they should come back to work,” said GAO spokesman Charles Young.

Outside the Capital Beltway, the budget battle loomed less large among federal employees.

“Once in a blue moon, we’ll exchange barbs and quips about the situation,” said Timothy Flavin, who handles disability claim appeals for the Social Security Administration in Rochester, N.Y. “They’re either apathetic, or they’re afraid to say anything,” he said of his colleagues.

Even if there is no last-minute agreement, Jan. 2 would not be doomsday because some cuts could be put off until later in the fiscal year. Most agencies would continue spending, but with caution, eliminating travel and training programs and slowing or halting hiring. Overtime would be phased out, as would temporary help. Managers may have to decide whom to furlough and for how long.

The Budget and Control Act of 2011 gives agencies 30 days to figure out exactly how they would juggle their finances, down to specific contracts and programs that would be eliminated. Union officials say they would demand bargaining over furloughs and possible layoffs. Unions would also want to bargain over the use of contractors to ensure they’re cut before federal employees.

Managers say that without knowing how long the cuts will be in effect, they can’t make smart decisions.

“As a manager, you’re effectively placing bets,” said Carol Bonosaro, president of the Senior Executives Association, which represents 7,300 top career executives in the government. “Do I start this contract or not start it? Let this vendor go?” she asked. “I stop training, but what if they don’t have that opportunity for a year? At what point do I say, ‘You’re not going’? ”

The Office of Management and Budget has instructed managers to consider furloughs as a last resort. But for agencies where labor makes up most of the budget, they would be hard to avoid.

“Employees understand that they will still be working on January 2nd,” said Patty Viers, a customer account specialist for the Defense Logistics Agency and president of Local 1148 of the American Federation of Government Employees. “But they’re getting more and more concerned about what’s going to happen in three months.”

Rosalind S. Helderman contributed to this report.