The government went back to work yesterday and showed little interest in assessing the impact of Monday's budget showdown that forced thousands of federal workers to abandon their desks in a move that cost Uncle Sam millions of tax dollars.

Top agency officials backpedaled on earlier estimates of the numbers of workers ordered home and downplayed the significance of closing so many federal offices in the middle of the day.

And, abandoning the complicated furlough guidelines, the officials embraced President Reagan's suggestion that everyone sent home be considered as having been on an extra day of paid annual leave, a term which usually refers to vacations.

Edwin Dale, a spokesman for the Office of Management and Budget, in effect summed up the government's attitude about gathering statistics on the cost and number of employes affected by Monday's furloughs, initially calling such information "too boring" and "yesterday's news."

However, after checking to see whether it was possible to come up with such data, Dale called a reporter back later in the day and said, "There is not and never will be an absolute, precise count and there is no need to (make one). There's no way to calculate the cost . . . It's perfectly clear there's no savings."

At the Office of Personnel Management, director Donald J. Devine expressed similar sentiments about analyzing what happened Monday, except to assure all workers sent home that they would be paid.

"Our major job is not to collect records but to keep the federal government working," Devine said. He called a news conference to explain that the continuing budget resolution that Congress passed late Monday contained provisions for paying the furloughed workers.

Asked if OPM would have a better contingency plan for furloughs on Dec. 15 if Congress still hasn't approved a permanent budget, the agency's Devine smiled broadly and said, "Yes."

Estimates of exactly how many government workers were sent home Monday varied. OMB, which earlier had said about 400,000 employes had been furloughed, revised that figure to around 200,000 yesterday. And OPM's Devine was reporting "something like half a million," until challenged by OMB's estimate.

"Well," Devine amended, "something less than half-a-million."

If the bureaucrats weren't hanging on every statistic, union officials and some members of Congress were.

Rep. Steny H. Hoyer (D-Md.) formally requested yesterday that the General Accounting Office make an official study of Monday's furlough experience and asked that the agency itemize the fiscal impact of the furloughs, payroll procedures and additional paperwork.

An aide to Sen. Alan Cranston, the only senator to vote against the continuing budget resolution, said the California Democrat was also interested in a GAO audit. Cranston says the furloughs cost the government at least $400 million.

Although GAO may be able to calculate the number of employes furloughed and some shutdown costs, a GAO official said, determining a final cost may be impossible because much of the expense is because of decreased productivity.

Others agreed.

"At a minimum, there's a full day of productivity lost, and it will probably take another full day to undo the effects of the furloughs," said Robert Honig, staff director of the Federal Government Service Task Force. Honig said it actually would have cost more to furlough government workers than to pay them because payroll computers would have had to be reprogrammed.

At the American Federation of Government Employees, the nation's largest federal workers union, spokesman Gary DiNunno said the furloughs probably had taken a mental toll on employes.

"The federal workers have been used as pawns," said DiNunno, whose union went to court to challenge the furloughs. The union argued that the furloughs were illegal since the union had not been consulted.

"Federal workers shouldn't be jerked around like this," DiNunno said, adding that the administration had had plenty of time to work out furlough plans with employe groups.

While officials and federal worker advocates argued over what had happened, however, most employes returned to their jobs as if nothing had happened, an informal survey indicated..

"It was hectic," one personnel official at the Agriculture Department said of the furlough orders, "but we've all gone back to our normal rush now."

But he, too, expressed the same lack of concern for evaluating the numbers of people affected.

"I have no earthly idea. I have not been asked to gather that information, and I won't until the request is made of me," said Ernest Toth, chief of staffing and personnel information at the agency.

At the White House, press spokesman Robin Gray said there was no way to know whether the American public called to praise or protest the administration's furlough order because the comments office, which tallies such calls, was ruled nonessential and shut down.

But not everyone at the White House stopped answering the phones Monday. When one congressional staff member called the White House press office, she said she was startled to hear a familiar voice -- ABC newscaster Sam Donaldson -- on the other end, giving her a rather boisterous report on the situation there.

"I answered the phones a little bit (at the White House press office). They were ringing off the hook," conceded Donaldson, who said he was careful to point out to callers that he did not work for the executive branch.

Besides the confusion, what many workers may remember best about Monday was being judged as essential or nonessential. Priorities at each agency were different. Somebody at the Veterans Administration, for example, thought it was an essential duty to dispatch a driver to pick up the administrator's new limousine.