Mayor Marion Barry proposed yesterday the most severe set of cutbacks in city services since home rule as he acknowledged that the city's budget shortage could be as high as $172.4 million.

The proposals, outlined to members of the District of Columbia City Council, would affect a sweeping array of city services -- from day care for the young to homemaker services for the elderly, from trash collections to food inspections, from summer school to snow removal.

The proposals would:

Eliminate 1,223 jobs from the city payroll, 550 of them through layoffs.

Cut 120 positions from the police department, including 90 uniformed police officers.

Close 21 recreation centers in public schools and reduce the hours of operation at 52 other such centers.

Reduce by about one month the time that city-operated outdoor swimming pool will be open this summer.

Reduce the number of slots in this year's summer jobs program for youth.

Cut by nearly one-fourth the number of city-funded jobs for hard-core unemployed adults with families.

In effect, cut the number of city personnel available for household care and companionship service for the elderly.

Barry and his advisers also are considering, as a second step to be announced within a week, an increase in property tax rates that could raise the average city homeowner's tax bill next year by $225.

The proposals come amid efforts to grapple with the city's budget deficit and to identify its dimensions.

Until now, budget director Gladys W. Mack had estimated the gap to be no more than $84.5 million. Yesterday, however, she outlined a list of much larger potential budget problems.

Mack said that $26.1 million would have to be saved through the program cuts or freezes proposed yesterday, and $92.6 million would have to come through additional revenues -- chiefly higher taxes and a supplementary U.S. payment.

The Barry administration already has made $12.7 million in program spending reductions. But the city may need as much as $41 million more if it is ordered to pay back money already collected through a tax on professionals that was ruled illegal last month by the D.C. Court of appeals.

The sharp cutbacks in services, many of which would hit hardest against the poor, the elderly and the unemployed, seemed somewhat out of character of Barry, a onetime militant social activist who sprang to political prominence as a spokesman for the neglected and an organizer of the hard-core unemployed.

The proposals did not conflict with the assertion that Barry made several times during his 1978 mayoral campaign and afterward that, on the issue of government spending, "I'm a fiscal conservative."

In disclosing his proposals yesterday, Barry said, "These have been difficult decisions which inevitably will cause some hardships on citizens, business, government services delivery, and on our employes."

Barry insisted that such cuts were necessary and not merely a bargaining position to win concessions from the City Council and Congress. The Council will have to approve the proposed tax increases and program reductions, while Congress will have to ratify supplemental spending proposals.

"I don't see any major disruptions," Barry said of his proposal. "There are some painful cuts in some areas, but not to the point where people are going to be hurt . . . I don't like it, but I don't think I have much of a choice. Believe me, this is serious."

The sharp service and personnel cuts would be only one portion of Barry's plan to keep the District of Columbia in the black throughout the current fiscal year, which ends Sept. 30.

Another major portion will be a hefty $24.1 million, six-month tax and fee package that was immediately attacked yesterday by City Council Chairman Arrington Dixon.

Besides the property tax increase, the mayor also is considering increases in the city's gasoline, hotel and deed recordation taxes and a new tax on the professional and trade services.

"There may be other approaches in terms of other ways that we can bring about savings in the government rather than go to the community with additional taxes at this time," Dixon said yesterday as he prepared to enter a closed door briefing that Barry held with the city's legislators.

"Many of us share concerns with the size of our government," Dixon said "and we think that size ought to be something that's looked at."

Many of the proposed reductions appeard to run counter to the nature of some festering problems in District unemployment, crime, and youth concerns.

Crime in the city rose 11 percent last year. Besides proposing the cuts in the police department, Barry also sought one of his largest reductions -- 400 positions -- in the Department of Corrections on the ground that it was guilty of overspending in the past.

Barry acknowledged that the reductions would decrease security, support and rehabilitation services at most city-run correction services.

Another continuing problem involves the city youth. Nearly half are unemployed and many more are idle. Barry proposed yesterday that 21 recreation centers in public schools be closed and that operations at 52 other centers by reduced by one or two hours each day. He also asked that city swimming pools be open from late June through August rather than the usual Memorial Day through Labor Day schedule.

Elderly persons are one of the fastest growing groups in the city. Barry proposed to freeze new homemaker and chore services, which provide companionship and household aid to many older Washingtonians. He also delayed the opening of a new elderly care center, the J. B. Johnson Home at 1st and K streets NW.

The single largest departmental cut came in the agency most often criticized for poor performance, the massive Department of Human Services. Barry planned freezes in day care and reductions in medical emergency room and outpatient payments.

He also asked to close several community health and mental health facilities this June, three months sooner than previously planned.

Barry recommended that the University of the District of Columbia cut back its summer school program and the D.C. school board also "adjust to today's fiscal realities" and make $6 million in cuts.

In the area of other city services, he proposed a 10 percent cut in the number of housing code inspectors, a delay in the opening of the Deanwood branch of the public library and decreases in security and the cleaning of city buildings and less regularity of street and alley cleaning.

Barry's message of hard times in the nation's capital was accompanied by a $107.4 million supplementary budget request seeking authority from Capitol Hill to spend $66.2 million more in operating funds and $41.2 million more in public works projects.

Most of that money, $61.8 million, would come in the form of a supplementary federal payment to the city. The federal payment is the U.S. government's annual allocation of funds to compensate the District of Columbia for the loss of revenue from tax-exempt federally-owned land and for the extra services incurred because Washington is the nation's capital.

Barry used the supplementary package to blame Congress for many of the city's budget woes and to ask establishment of a fixed formula for the payment.

"Many of the District's budgetary difficulties may be tied directly to an under-funded federal payment," Barry said. "In future years, a predictable, formula-based federal payment level should be developed to overcome the budgetary problems which ensure from a shrinking and unpredictable federal payment level."

The biggest item in the supplemental budget would be $30.7 million for employe pensions, public assistance and related programs. In addition, $16.2 million is sought to finance the payment to city workers of the same 7 percent pay rise that federal employes got last October. Another $13 million would pay the higher costs of energy used by city buildings and programs.