Washington, the company town run by politicians and held together by bureaucrats, suffered through an unnerving payroll crisis yesterday that virtually shut down some agencies and sent thousands of confused federal workers home by mid-day.

As many as 180,000 area government workers, part of an estimated 500,000 federal employes hit by President Reagan's funding veto, were abruptly furloughed throughout the city after agency chiefs determined that their government services were "nonessential."

The temporary lay-offs caused widespread confusion throughout the federal bureaucracy. Some agencies, like the Pentagon, were untouched and carried on with business as usual. Many others were hit hard; the Department of Agriculture, for example, sent half its employes home at noon.

Stunned by Reagan's actions, hundreds of workers flooded federal credit unions, jammed government switchboards with questions about pay and benefits and quickly juggled or canceled their Monday appointments, meetings and lunch dates.

By late afternoon, much of the morning's confusion and panic had turned mellow, even festive, for some, as Congress moved toward a makeshift resolution of the budget conflict that apparently forestalled further problems until Dec. 15. The unexpected "early slide" suddenly meant a chance to rush home and watch a favorite soap opera, get an extra drink or see a movie while waiting for the commuter bus home.

Before the payroll difficulties had been eased, the reaction of federal workers had ranged from anger by some and delight by others at the prospect of a few days off before the Thanksgiving holiday. The degree of alarm seemed to depend on the state of one's finances rather than the state of the union.

"I'd like a furlough now, I've got a lot of house and yard work to do," said a cheery Marrianne Ahmad, an employe at the Department of Health and Human Services who has worked for the government for 18 years.

For Rita Villella, a wildlife biologist at the Interior Department, the order to go home at 2 p.m. was a paycheck-threatening announcement that she feared could threaten her rent payment. Villella, 27, had another problem with the characterization of her work as nonessential.

"I don't like the way it sounds," she said. "I'd like to think we're doing some good work here."

Although the budget impasse between Congress and the president had been building all last week, most veteran federal workers -- accustomed to yearly budget tugs-of-war -- assumed this latest squabble would be resolved routinely. Until yesterday.

"I really didn't think it would get this far," said Larry Collins, a Department of Agriculture employe who has been a government worker for 27 years. "I figured it would be resolved by now. The man Reagan made history."

For federal workers, that history included rumors, contradictory information, confusion, and the dispirited feeling of being caught in the middle of a conflict that was not of their making. And the situation didn't do much for government car pools, either.

"I can't go home yet," said one woman who answered the telephone at the Internal Revenue Service after most everyone else in her office had cleared out. "The guy who drove today is essential."

Walter Okamoto, 39, spent a very long lunch hour in the basement cafeteria at the Interior Department, waiting for official word on whether he was being sent home. The question was one of some urgency since Okamoto, who injured his leg recently and is on crutches, was hoping to catch a ride with his van pool back to Warrenton, Va.

"As of noon, they've all been put on leave without pay, and they're just waiting for me," said the 15-year government veteran, who was furloughed at 2 p.m.

For the federal workers who began streaming out their offices and into the streets between noon and 3 p.m., going straight home was not necessarily their first impulse. Many lingered on the doorsteps of their agencies, uncertain about what to do and where to go.

Not everyone had that problem.

"I'm going to a movie -- either the French sex comedy or the Italian sex comedy," said one employe at the Environmental Protection Agency, who was looking forward to the day off.

Delba Durrough was sent home from the Commerce Department at noon with the advice to listen to the news for information about when to come back to work. She called the furlough decision "raunchy" but was cooling her anger with plans to "go home and watch 'General Hospital.' "

Low- and mid-level workers weren't the only ones caught off guard by the sudden furloughs. Several of the government's top officials, including Vice President Bush, discovered they, too, were subject to the guidelines governing essential and nonessential business.

Bush had to cancel a scheduled business trip to New York because of the absence of operating funds, and about 75 percent of the vice president's staff was sent home by noon.

The public comment line at the White House, where 150 of the 351 employes were furloughed without pay, was answered by a recorded voice yesterday afternoon: "The White House is involved in an orderly phase-down," it said without apology. "No one is here to answer your call."

In California, Attorney General William French Smith was scheduled to give a talk yesterday morning to a law enforcement group. He canceled the speech and flew home to Washington after deciding that "this type of activity wouldn't be considered essential," according to a Justice Department spokesman.

Some workers, including a number of those sent home yesterday, had nothing but praise for Reagan, arguing that the furloughs could have been avoided if Congress had gone along with the president's budget cuts -- but union spokesmen and others workers, particularly in agencies already beset by program cuts and reductions-in-force, angrily called Reagan's furlough order a political ploy aimed at creating enough chaos to force Congress' hand.

People in Washington were not the only ones affected. When 500 college officials arrived in town to attend a special two-day conference on minority aid, they were chagrined to learn that the meeting was off because the Department of Education, sponsor of the event, was shutting down.

"I'm not surprised anymore by anything the government does or doesn't do," said Jane Forni of Marymount College in Tarrytown, N.Y. "It'd be sad to think of the government shutting down if it weren't so ridiculous."

At times, some of the reports from the agencies did seem humorous, or typical.

From Agriculture: "You could shoot a gun down the hall," said Deputy Agriculture Secretary Richard E. Lyng.

From Goddard Space Flight Center in Greenbelt: "Things happen up there" in space. Satellites "belch and change orbit, and then it's hard to pick them up again," said spokesman James C. Elliott, who added his workers were so busy tracking 27 of them that no one had time to check if they should be on the job.

At the CIA: "The only thing we're saying at this point is that the CIA is in the category of an essential national security operation," spokesman Dale Peterson said. Did that mean no one was furloughed? "That's the only statement we're making at this time."

One of the best examples of furlough surprise occurred at the Federal Communications Commission, where an advisory committee on minority group activity in telecommunications gathered for a long-scheduled meeting, took a lunch break and returned to find themselves locked out of the building.

Throughout the government, workers who tried to get some information were frequently frustrated because the people they contacted were almost as much in the dark or busy trying to help draft solutions to the budget impasse.

The Federal Government Service Task Force chaired by Rep. Michael D. Barnes (D-Md.) received more than 8,000 telephone calls by 3 p.m. from worried federal workers who had heard all manner of rumors about what was going to happen to them.

Some of the problem could be attributed to conflicting information that was handed out during the day.

"I got a call telling me to go home at noon, and then the same person called back a few minutes later telling me to stay," one Treasury Department worker complained.

At the Interior Department, an agency memo suggested that workers serve on a voluntary basis without pay and noted that, in the past, retroactive pay was routinely approved after such funding cutoffs.

The Office of Budget and Management was quick to contradict that suggestion, pointing out that it is illegal for furloughed workers to come to work voluntarily. The Office of Personnel Management added its own confusing interpretation by saying it was illegal for bosses and supervisors to know about volunteer employes, but not illegal for the employes to show up.

One OPM worker, for example, was declared nonessential but had planned to come into work anyway in order to send out a list of other nonessential employes.

Despite a day of mounting confusion there were some government functions that went on as usual, their feelings of essentialness intact.

The Treasury Department continued to print money and collect taxes, and, at the National Zoo, a spokesman reported reassuringly, "We expect to remain open and all the animals will be fed."