The chairman of the city council's finance committee urged Mayor Marion Barry yesterday to make a clear public statement on the city's long-term financial prospects, charging that "the council is being totally snowed on the financial condition of the city."

Council Member John A. Wilson (D-Ward 2), the finance committee chairman, faced off against Barry's budget director before a meeting of the full council.

It was the first briefing of the council on the city's financial condition since City Administrator Elijah B. Roers sent shock waves throughout city agencies on Jan. 23 with a directive that they find ways to trim $28 million from their spending between now and Sept. 30 to make up a prospective deficit. f

Budget Director Gladys Mack defended the validity of the $28 million figure against estimates by Wilson that the deficit could rise much higher. She told the council that responses from department heads indicate the city can meet the cutback goal without seeking a bail-out from Congress.

Mack said yesterday that the actual cuts will be decided by the mayor and reviewed, probably informally, by the council.

She said department heads have replied with indications that the cutback can be achieved chiefly by not filling jobs that become vacant during the balance of the fiscal year.If jobs are vacated at an annual rate of only 2 percent, about one-third of normal, that alone would bring a saving of $22 million, she said.

Personnel costs are most vulnerable to cutbacks because they represent about half the $1.4 billion appropriated budget and because the levels of city programs are largely fixed by other laws, city officials say.

Wilson did not attempt yesterday to win anybody's acceptance of an earlier estimate he made that the city's deficit would reach $146 million.

"Call it anything from $29 million to $146 million -- probably it is a number in-between," he said.

Whatever the actual figure, Wilson said it foreshadows the need for a tax increase for the 1982 fiscal year so great that it would be politically unthinkable.

The proposed 1981 budget, soon to be submitted to Congress by President Carter, contains no major tax rise. The city's 1981 fiscal year begins Oct. 1.

Wilson said officials like Mack will not have to answer to the citizens, so Barry must speak out clearly. Barry said last night through his press office that the situation is "serious but not a crisis at this point," and that Mack and Rogers are being paid to make recommendations to him.

Wilson, whose seat is up for election next fall, first made his own $146 million deficit estimate at a hearing of the finance committee last Thursday.

Mack, while agreeing with Wilson's arithmetic in tallying city obligations, cast doubt on the meaning of his total. She said Wilson was in effect double-counting some expenses and ignoring some offsetting receipts that are included in the official projection of $28 million.

For example, she said her projection, unlike Wilson's, assumes that Congress will grant a supplemental appropriation covering $15 million in unfunded pay raises for city employes and $21 million in added pension costs imposed on the city by Congress last year.

Money to finance the supplemental budget would come from $62 million authorized as the remainder of this year's federal payment to the city. A payment of up to $300 million is made each year to reimburse the city for taxes it cannot collect on federal property and the costs it incurs in its role as the nation's capital.

The pay raises represent the difference between a 5 percent increase included in the city budget and the 7 percent increase granted by the city when it matched the presidentially approved increase for federal workers.

(The council, at Barry's request, added another item yesterday to the supplemental request: $647,000 to cover police overtime pay and other extra municipal costs resulting from the three-day visit of Pope John Paul II last October.)

Mack said the city expects to be able to repay, without increasing the deficit, 120 million it had borrowed from the U.S. Treasury last year to meet short-term expenses, and to pay $23 million to Metro for operating subsidies. Both were on Wilson's list of city obligations.

Mack also said Wilson was wrong in listing a potential $45 million refund of taxes on the earnings of professionals who live in the suburbs and work in the city.

A Superior Court judge ruled last April that the tax is illegal and must be refunded. The city has collected the tax while appealing that decision to the D.C. Court of Appeals. Even if the city loses, Mack said, the refund would come in future years, not this one.

Mack and other city officials said the financial problems are exacerbated by the great time lag between the preparation of the budget and its enactment by Congress.

The process, involving reviews by the mayor, the council, the White House and ultimately by Congress, takes more than two years. Walter E. Washington, who left office 13 months ago, was still mayor when the current budget was being put together.

By contrast, it takes many cities and counties as little as 60 days between the presentation and adoption of a budget by the local government body.

D.C. Auditor Matthew S. Watson said one local problem is budgeting that is too "tight" -- that is, high estimates of revenues and low estimates of costs, leaving little cushion.

Mack said the city had hoped to cushion this year's budget with a $44 million cash balance left over from 1978. But she said congressional budget-cutting and a court ruling that overturned a change in the way the city collects taxes on large commercial property owners wiped out all but $5.9 million.

Meantime, costs have gone upward beyond the city's control. One official said the cost of heating oil already will exceed the budget by $2.9 million and may reach as high as $5 million by the end of the fiscal year.

Spokesmen for the two congressional D.C. Appropriations subcommittee chairmen, Sen. Patrick J. Leahy (D-Vt.) and Rep. Charles Wilson (D-Texas), said city officials are right in not asking Congress to rescue the city with federal money.

"If they (city officials) come up with revenue estimates and we approve a program, and if the revenue estimates turn out wrong, we think it is up to them to make the corrections," said John Gnorski, Leahy's Senate budget staff chief."The first course of action (by the city) should not be to come up here for a bail-out."