If cities were private companies, the District of Columbia would be Chrysler.

Deeply in debt, operating at a mounting deficit and laying off workers to pinch pennies, the District stays solvent only as long as it is able to borrow. Unlike Chrysler, the city borrows from the U.S. Treasury instead of from private banks, and Uncle Sam has been a lenient creditor. But 1981 could be the year the string runs out.

Throughout 1980, the administration of Mayor Marion Barry scrambled to shore up a crumbling fiscal edifice, only to be buffeted by unforeseen reversals. In July, Barry proposed a complex long-range plan for refinancing the city's debts and reducing deficit spending -- a plan devised primarily by the New York investment banking house of Lazard Freres & Co.

But none of the components of that plan has been put into effect -- except the adoption of a budget for the 1982 fiscal year that is theoretically balanced -- and city officials have begun to warn that the District could actually run out of cash by next summer.

For most of the past year, they argued that paper deficits and accumulated liabilities would not be translated into a cash-flow crisis that would cause the city to miss payrolls or suspend welfare checks, but by December they conceded that a cash crunch could be developing.

The District at the end of 1980 suffered from two separate but interlocking fiscal ailments, one short-term and one long-term. The cure for one depends on the cure for the other. Either could be fatal to the overriding objective of setting the city on its feet as an indepedent financial entity, capable of borrowing on the commercial markets from which it has always been excluded. In the immediate future, the most urgent problem is a looming shortage of operating cash.

In past years the city always has borrowed from the Treasury the short-term cash needed to pay bills in the intervals between major tax collections. Those loans are interest-free, but the city has to pay them back at the end of the fiscal year. This could be the year when the need for cash is greater than the amount the city can borrow in that manner and hope to repay.

Barry plans to ask Congress for legislation that would authorize the city to borrow $215 million from the Federal Financing Bank, an arm of the Treasury.

The money would be used to pay cash debts that have simply been rolled over from previous years and to cover a $41 million payout the city is committed to make in April to refund an illegal tax on the incomes of nonresident professionals.

But skeptics such as City Councilman John A. Wilson (D-Ward 2), chairman of the council's Finance and Revenue Committee, say that the plan will not be approved and the city will be forced to impose massive tax increases to cover its liabilities.

Several taxes, including the general sales tax and the commercial property tax, were raised last summer. Barry, agreeing with the argument of the Board of Trade and others in the business community that the city already is "taxed to the limit" says he wants no more increases for at least two years. But with costs rising faster than revenues, Barry may be forced to call for a tax increase if Congress fails to act on his revenue proposals.

The legislation that conferred partial home rule on the District envisioned the end of the city's unique financial relationship with the Treasury, the District's sole source of credit. In addition to the interest-free cash-flow loans, the city gets all its capital funds from Congress, at interest rates several costly percentage points higher than it would have to pay if it could issue tax-exempt municipal bonds in the commercial market.

But the chaotic conditions of the city's financial records made it impossible for auditors to issue the kind of reports that would satisfy bond-rating agencies, and the District has stayed out of the market while its Treasury borrowing authority has been renewed year to year.

The work of the accounting firm of Arthur Andersen & Co. in straightening out the city's books is expected to produce the first unqualified audit in February, but unfortunately for the city, the conclusions that Andersen's accountants came to in their analysis were not encouraging.

They found that the District's cumulative deficit was $284 million as of Sept. 30, 1979, not counting hundreds of millions of dollars in unfunded pension liability for city workers. Another deficit in the fiscal year that ended Spet. 30, 1980, estimated to be $125 million, brought the total to $409 million. Of that amount, Anderson's accountants and city officials calculated that $215 million represented actual short-term cash needs.

The city has not enumerated all the components of that $215 million, but it includes nearly $50 million owed to the Federal Bureau of Prisons and St. Elizabeths hospital for housing D.C. residents, and the $41 million that will be needed April 1 to repay the tax on the incomes of nonresident professionals.The federal agencies are not dunning the city for the money -- a good example of how a debt to Uncle Sam is an easier burden to bear than a debt to a syndicate of banks -- but the city's advisers from Lazard Freres want those books cleared so the city will receive a good rating when it finally offers its bonds on the market.

The professionals' tax refund, however, is a cash obligation that cannot be avoided. The city is legally obligated to pay it April 1. Lawyers for the professionals -- dentists, doctors, architects, lawyers and others who live in the suburbs and work in the city -- were told that the money would come from property-tax collections due in March. But that tax money already is earmarked for other expenditures, and if it is not replaced in the city's coffers by borrowed funds, the city could finally face the specter of payless paydays.

City workers already are disgruntled because Mayor Barry and the City Council gave them a cost-of-living salary increase of only 5 percent this year, while their federal counterparts received 9.1 percent. Unions representing the workes have gone to court asking that pay raises be made comparable or that the mayor at least be required to negotiate with the unions. If they triumph in the court case the District could be forced to come up with another $28 million, Barry says.

Barry's proposed budget for the 1982 fiscal year contained no funds for a workers' pay increase; the mayor said additional revenue from legislation he hoped Congress would enact this year could be used for salaries, but without that, no money would be available. The City Council, agreeing with Wilson that some raise was inevitable, especially since the workers are now entitled to collective bargaining, amended the budget to set aside $26 million for that purpose.

But that created a new problem for Barry and his financial advisers, because the City Council would get most of those funds by diverting $20 million that Barry had proposed to set aside to begin repaying the proposed $215 million loan from Congress that he says is essential to meet cash needs in the current year. That left the city in the position of either not borrowing the cash it needs to keep going, or getting the loan without knowing if funds will be available to repay it.

Some council members defended their move by saying that the $215 million loan was not a reality and that legislation authorizing it had not even been submitted to Congress, let alone enacted. But only Wilson went so far as to say publicly that substantial tax increases were the only alternative to the council members' proposal.

In fact, if the $215 million loan is not approved by Congress, Barry would happily settle for another piece of legislation that he regards as even more vital to the city's long-range fiscal health. That is a measure to raise the annual federal payment that Congress makes to the city in lieu of taxes on federal property. The current maximum annual federal payment is $300 million. Barry favors a formula that would set it at a fixed percentage of the city's local tax revenues.

A bill introduced by Rep. Ron Dellums (D-Calif.) and D.C. Del. Walter Fauntroy would have set it at 43 percent of tax revenues. If enacted, that would have added about $75 million to the city's anticipated revenues this year. But the bill never attracted much support and died with the adjournment of Congress.

The city's overall financial picture remains clouded. For example, the city proposes to finance its growing Metro transit-subsidy obligation by persuading Congress to authorize re-enactment of the nonresident professionals' tax -- an unlikely eventuality. But at the same time, there are potential bright spots that could bring the city back from the brink and establish a solid footing for eventual withdrawal from the Treasury and entry into the bond market.

One is a new law authorizing the city to seize dormant bank accounts. That could result in a $30 million windfall, more than offsetting the loss of revenue incurred when the city's ill-fated gasoline sales tax was repealed. Another is the city lottery, approved by the voters in a referendum in November; its supporters say it will generate $34 million in revenue in its first year and more in later years. A third is the convention center, now under construction downtown, which city officials expect to have a dramatic impact on sales, hotel and restaurant tax revenue when it opens in the summer of 1982.