The Gramm-Rudman-Hollings budget cuts unveiled this week hit the District of Columbia the hardest of any area jurisdiction, with surrounding areas largely spared because their finances are not as dependent on the federal government, according to local government officials and analysts.

St. Elizabeths Hospital in Southeast Washington, jointly financed by the city and the federal government, would be particularly hit hard by proposed cuts of more than $5 million in the fiscal year that began Oct. 1. City officials said yesterday the future of the hospital may be jeopardized by the federal government's failure to provide as much funding as promised under a carefully crafted 1984 agreement for transfer of the hospital from federal to city management.

"If the federal government doesn't live up to its participation, we would have to rethink what we are doing," Mayor Marion Barry said during an unannounced appearance at a City Council hearing on the District's recently announced plan for a new mental health system for the city.

The automatic 4.3 percent cuts in domestic programs for fiscal 1986, announced by federal budget offices on Wednesday, will cause problems for only a small number of suburban areas, said Philip Dearborn, vice president of the Greater Washington Research Center.

"The suburbs don't like to lose federal aid, but in terms of their budgets it is not going to affect planning all that much," Dearborn said. "The District, though, we are talking about a third of its revenue coming from federal aid. They really have to worry."

The proposed cutbacks would take effect March 1 unless the president and Congress agree on an alternative plan.

District officials expressed alarm this week that the federal government intends to take back $23.5 million of the $547 million federal payment already granted to the District for the current fiscal year. Barry said that action could force "serious reductions in our budget . . . . Children will suffer, seniors will suffer, public housing will suffer."

Suburban officials, meanwhile, said yesterday that reductions forced by the Gramm-Rudman-Hollings deficit reduction legislation could curtail growth of transportation systems -- particularly the Metro subway.

Charles W. Gilchrist, Montgomery County executive, said that the federal law "is now being used as an excuse for further withholding funds that have already been appropriated for Metro."

"Our Wheaton line, between Silver Spring and Wheaton, is being held up day by day because of failures to distribute funds that already are due," he said.

The Washington Metropolitan Area Transit Authority is programmed to lose $1.1 million of the federal funds already approved for it in the current fiscal year, according to documents prepared by the Office of Management and Budget and the Congressional Budget Office. However, the OMB recommendation for the next fiscal year calls for a complete halt to federal funding for the transit system, endangering plans to complete the Red and Green lines.

Beyond the problems facing Metro, local budget and program officials said it is too early to estimate with certainty the impact of the first round of the federal cuts. Absolutely crucial, they said, is how the elimination of funds filters down into specific programs.

"I don't think anybody is going to panic or react until we know a little more," said Shiva Pant, head of the Fairfax County Office of Transportation.

The metropolitan area's financially well-off counties receive relatively little federal aid. Fairfax County calculates that only $45 million of its $1.4 billion annual budget, or about 3 percent, comes directly from the federal government. Only $51 million of Montgomery County's $967 million operating budget comes from federal sources, or5 percent of the total.

Dearborn estimated that even a less affluent county such as Prince George's, which is more dependent on federal assistance, still receives no more than 8 percent of its operating budget from the federal government.

The District's base of funding is especially vulnerable to Gramm-Rudman-Hollings cutbacks because of its extraordinary dependence on the federal payment, which historically has reimbursed the city for the cost of services provided to the federal government, whose property is exempt from local taxes.

The payment, scheduled to be reduced by 4.3 percent, includes the federal government's $425 million payment in lieu of property taxes, as well as payments for water and sewer use, corrections programs, retirement programs and $25 million earmarked to help finance the gradual transfer of St. Elizabeths to the District.

Virginia Fleming, director of the D.C. mental health system reorganization office, said yesterday the city could not make up for the lost federal funds for the hospital and that the cutback might result in St. Elizabeths becoming a smaller, overcrowded hospital in jeopardy of losing its accreditation.

The federal cutback also might result in the layoff of hospital staff and the closure ofsome of the buildings in the hospital complex, she said.

The hospital's current annual budget totals $132.9 million, including federal and D.C. revenues. But under a 1984 agreement, the District is to take over managing the hospital in October 1987. The federal government agreed to provide funding for the hospital and a special subsidy to the District through 1991 to aid in the transition.

Under cuts revealed this week, a federal appropriation for St. Elizabeths would be reduced by$4.8 million this year, on top of the reduction in the part of the federal payment earmarked for St. Elizabeths. Coming together, those reductions could have a devastating impact on the hospital, city officials said.

The amount of the hospital's budget subject to the Gramm-Rudman-Hollings' automatic cuts was in dispute, however, and federal officials had internal debates yesterday over whether the designated cuts should be $1.9 million rather than$4.8 million, accourding to sources. But an OMB spokesman said his agency is standing by the original figure.

City officials spent more than a year preparing a transition plan for St. Elizabeths Hospital, envisioning a facility about half its current size and with about half the current 1,600 patients.

Fleming and other city officials denounced the federal government for going back on its promised funding, which had been negotiated in 1984 by the District and OMB before being approved by Congress.

"They are abandoning their responsibility sooner than their planned timetable," Fleming said. "We will have to go back to the drawing board."