Buffeted by setbacks in Congress and the courts, rising costs and unforeseen expenditures, officials of Mayor Marion Barry's administration still believe the city can stay solvent and keep paying bills through this fiscal year -- if.

What comes after the "if" depends on who is doing the analysis. Holes big and small have been punched in the fragile edifice, and some major infusion of outside aid will almost certainly be needed next summer. But the city officials responsible for managing the cash insist the District's mounting deficit and gloomy long-range financial outlook need not result in any missed paychecks or government shutdowns this year.

"It's like the Chrysler Corp.," one said. "The company was losing record amounts of money, but workers and suppliers still got paid. We have something like that here. Our deficit is getting bigger, but we still have cash to operate with" because the city still has a source of credit.

One of Barry's problems is selling his financial program to city workers, the City Council and the public has been to convince them that a true crisis exists when the city government seems to roll along without missing a beat.

Some workers have been laid off, some supplies have dwindled, but all payrolls have been met, loans have been repaid on schedule and essential services have been maintained. Recent events have made it more difficult to keep up that balancing act for the rest of this year. Barry's aides say there could be a crunch next summer that will make unhappy believers of the skeptics, but they argue that by anticipating the crisis they can maneuver to fend it off.

In recent weeks, the city's carefully drafted spending program for this year has been eroded by several events:

The District committed itself in court to repay on April 1 nearly $41 million that was collected in earlier years from an illegal tax on suburban professionals. There is no money in the budget for that payment; but the commitment is binding and means the funds must be borrowed or diverted from other programs.

A judge ordered the city to reopen a health clinic in Northwest that had been shut to save money.

The Department of Employment Services notified the Budget Office that it anticipates spending at least $3 million more than it has been allocated this year for the disability compensation program which is mandatory. a

Congress required the District to increase the police force by more than 250 officers.

The unions representing city workers said they would go to court to seek full wage parity with federal counterparts. A ruling in their favor could cost the city more than $25 million in unbudgeted outlays.

The City Council, at Barry's request, repealed the 6 percent sales tax on gasoline, leaving a gap in anticipated revenues of about $9 million.

Nevertheless, "We are going to make it," said City Administrator Elijah B. Rogers. "We are not going to run out of cash."

"Nobody should tell you that there won't be some crunches, because there will," said Ivanhoe Donaldson, acting director of the Department of Employment Services and a member of Barry's "cash-management team." The city, he said, "can make plans to face a coming crunch and not get caught by surprise like the Chicago schools," which were forced to close briefly when they ran out of funds. "We know what our problems are going to be and what our potential options are."

The District's $1.5 billion operating budget is technically balanced; anticipated revenues match anticipated outlays. Even before repeal of the gasoline tax, however, knowledgeable officials such as John A. Wilson, chairman of the City Council's finance and revenue committee, were questioning the validity of the revenue assumptions.

Regardless of whether the projections are accurate, the city's revenue does not flow in evenly. The coffers are full in September and March, when semiannual property tax payments are made, but often close to empty in between. Traditionally the city has taken out interest-free short term loans from the U.S. Treasury -- its only source of credit -- to get over those periods.

Those loans are supposed to be paid off at the end of each fiscal year. They are made in anticipation of revenue, and when the revenue comes in it is used to repay the Treasury. The issue facing the Barry administration this year is whether it can survive through the low-cash period next summer, before the September tax collections are received, without borrowing more than it can repay.

Barry, Rogers, Donaldson and assistant City Administrator for Financial Management Edward Winner say yes. But their answer presumes the city will be able to get at least some of the $21.5 million in extra cash Barry has proposed to borrow from an arm of Treasury. That loan would be different from traditional short-term borrowing in that it would not have to be repaid this year. Congressional action is needed to authorize it.

"Our assumptions are based on at least some portion of that $215 million," Donaldson said. "It would cover the professionals' tax refund. The question of how much extra cash we really need won't be answered until Februrary," when an auditor's report reveals the scope of the city's deficit for the last fiscal year, which ended Sept. 30. At the end of that year, the city dipped into tax revenue to repay $60 million to Treasury, while other bills estimated to total at least $100 million were left unpaid.

"We're in relatively good shape," Rogers said, "but without some of that $215 million, it's going to be tough. There might be some major shortfalls. Maybe there will have to be another hiring freeze or some cutbacks in expenditures. But we can make it. We have to make it."

The commitment to repay the professionals' tax is ironclad, Rogers and Barry said. "That's why I need that $215 million loan," Barry said in a recent interview. Without that, he said, the professionals' refund will have to come "out of the system," which would mean that $41 million worth of bills would be rolled over into the 1982 fiscal year when the process would repeat itself.

Legislation authorizing the special $215 million loan to cover current and past deficits will be introduced in the new Congress in January. Even if it fails, however, some things could still happen, making it difficult to predict just how deep the crisis will be next summer.

Some of the professionals might not claim refunds, reducing the outlay. A city lottery, approved by voters in a referendum last month, could be operating, bringing in an infusion of new cash. A new city law authorizing seizure of dormant bank accounts, if allowed to stand by Congress, could produce a windfall of up $30 million or more. Or the City Council, against Barry's wishes, might vote a tax increase.

Meanwhile, city officials agree, Washington -- despite its growing deficit -- does not face the problems that provoked crises in New York and Cleveland because it has issued no bonds and borrowed from no banks.So it is not under any pressure from creditors, and as long as it has its open window at the U.S. Treasury, it can stave off insolvency at least in the short run.