Mayor Marion Barry, acknowledging that the District of Columbia fiscal crisis is worsening and that by October the city's deficit will have ballooned to $409 million, yesterday proposed a financial rescue plan that leans heavily on the federal government.

Speaking in a long-waited, televised speech, Barry painted a bleak and uncertain portrait of the city's financial future in which austere conditions would become a fact of life and city residents would spend the next 30 years paying off accumulated and current debts.

To resolve the $409 million deficit, Barry proposed first borrowing $215 million from the federal Financing Bank, an arm of the U.S. Treasury that buys securities from federal agencies.

Such a bond sale would require the approval of the City Council and Congress. The District would agree to pay off the loan plus interst in $20-million-a-year installments over the next 30 years.

To cover the remaining $194 million in the overall deficit, the mayor recommended that the District government set aside $10 million each year for 20 years, beginning in late 1982.

He proposed no new or increased taxes on District residents through 1982. But to balance the city's budget in 1982, the mayor said, drastic -- but undisclosed -- program cuts would be necessary and 2,100 more city workers would lose their jobs.

That would bring to 6,500 the number of employes to be cut from the District's regular work force of 35,000 through fiscal 1982. Barry announced earlier this year that he would cut 1,540 jobs by October and plans to cut another 2,860 during the 1981 fiscal year.

Barry also asked Congress for an increase in the yearly federal payment to the District -- a position long held by the city government. The payment is now authorized at a maximum of $300 million a year, but Congress has never appropriated that full amount. The mayor said he supports pending legislation that would effectively nearly double the payment.

Over and above the payment, Barry urged that Congress pay an additional $175 million a year for the next 29 years -- a total of $5.1 billion -- to cover unfunded pension liabilities for city workers that he said were incurred before the city obtained limited home rule in 1975.

Charged by Congress to identify "stable and reliable" sources of funding for the District's share of Metro costs, Barry proposed reimposition of a tax on the incomes of nonresident professionals who work in the District -- similar to a tax struck down by the courts in February. He also suggested higher Metro fares and decreased bus service.

The Mayor's speech, accompanied by the release of a two-inch-thick financial plan for the next three years, left unanswered many questions uppermost in the minds of many District residents. He did not spell out what services would be cut or whose jobs would be lost in the proposed drastic budget cutbacks for 1982.

Barry said the city will end the current fiscal year with a deficit of $125 million, which will be added to the $284 million accumulated in past years, making the $409 million total. Despite this, the city will not default on any of its obligations, officials said. The bills will be carried over into next fiscal year.

It was the fourth plan Barry has offered to solve the budget crisis, but key officials acknowledged last night that they could not guarantee that it was definitive.

In January, acting through City Administrator Elijah B. Rogers, the mayor imposed spending cutbacks to eliminate a deficit, then estimated at $28 million. On March 6, he pegged the deficit at $172 million and vowed to eliminate 1,223 city jobs and further decrease spending. On April 24 in what was called a "major address" at the Martin Luther King Jr. Library, Barry raised the number of jobs to be eliminated to 1,540.

Barry also had proposed $20.2 million in new and increased taxes, most of which the City Council finally approved, reluctantly, on July 1. But the mayor's budget plans were dealt a blow when Congress approved only about two-thirds of a $61.8 million supplemental federal payment Barry had requested.

Meanwhile, the austerity measures drew protests by police and firefighters. Groups ranging from senior citizens to day-care mothers with their infants came to the District Building to demonstrate and gasoline dealers shut down their stations to protests a new gas tax. Barry's political base seemed threatened on all sides.

The mayor said yesterday's proposals constituted a "comprehensive plan" for curing the ailing city budget, but aides told reporters that Washington residents will have to wait until September, when Barry submits his 1982 budget, for specifics on cutbacks and layoffs.

Seated at his desk in front of an African wall hanging and with a copy of the thick financial plan at his fingertips, Barry said that the city's budget crisis comes at a time when other cities and even the federal government are hard-pressed to handle "alarming" increases in the cost of providing services and as a recession has bitten hard into revenues.

In addition, he said, the District's problems are compounded by the federal government's continuing involvement in the city's budgetary process.

"In spite of the economy, and in spite of the restraints, we can restore fiscal health to our city," Barry said. "We can, we must, and we will."

While Barry's presentation was critical of the federal government for helping to create the budget crisis, at the same time it proposed profound long-range commitments to the city on the part of both Congress and the White House.

"It is important to realize that $179 million (of the $409 million accumulated deficit) occurred before home rule began in 1975," Barry said. "This means that the city can justifiably make the case that the federal government owes the District at least $179 million."

But Barry and his aides were strident in maintaining that the plan does not constitute a federal "bail-out" of the kind developed to save New York City from bankruptcy.

They pointed out that the $215 million federal purchase of District of Columbia bonds does not remove from the District the responsibility of eventually repaying the money.

However, it is an option not available to other cities, since Barry's argument in favor of the plan is that Washington was treated for 200 years like a federal agency and should be able to exercise this borrowing right reserved for federal agencies.

In addition, according to the plan, the city wants to seek a lower-than-usual interest rate of around 8 percent keyed to a municipal bond index. The effect would be to have it both ways to enjoy privileges of both a federal agency and an independent municipality.

Barry's plan states that the annual $175 million payments from Congress over the next 29 years to cover unfunded pension liabilities is necessary because an earlier congressional payment plan, calling for payment of $1.3 billion over the next 25 years, will actually fall far short of the amount required. The requested payments total $5.1 billion.

In addition, the plan says, the mayor is considering other alternatives to avoid an estimated $164 million budget gap in 1982 if current levels of spending are maintained. These include $37 million inservice cuts and no cost-of-living pay increases for city workers. This could mean two years in a row in which city workers would not receive a pay increase.

Despite the mayor's prediction of a $125 million deficit during the current fiscal year, City Administrator Rogers told reporters that the city may not have to borrow more money from the U.S. Treasury to meet its payrolls and other obligations between now and Sept. 30. The city already owes the Treasury $60 million.

The $125 million is made up chiefly of three major items -- a $35.6 million "underfunding" of various of city programs by Congress, which created an actual cash drain; $39.3 million the city owes but does not yet need to pay because it lost several court cases, including the invalidation of the tax on professionals; and $28.5 million that must be entered as a liability on the city's books because of a change in city accounting procedures.

Barry's plan does not directly affect the city's proposed budget for the 1981 fiscal year, which the mayor trimmed by $61 million after it was submitted to Congress in January. The amended budget, totaling $1.44 billion, in now pending in Congress.

At current service levels, Barry's plan states, the 1982 budget would grow by 16 percent over the 1981 budget,reaching $1.67 billion. Barry said he plans to hold the increase to 5 percent, which would bring the total to $1.51 billion.

"In the 19 months that I have been your mayor, in spite of all the financial problems we have faced your government has continued to provide basic and necessary services," Barry said in his televised speech. He promised that the government would continue to meet its payroll, meet "our commitment to the poor," and work . . . to improve the quality of education for our children."