President Ronald Reagan politely preached to America last Thursday night on the theme of reduced government spending, employing a vivid metaphor. "Well," he said, "We can lecture our children about extravagance until we run out of voice and breath. Or we can cure their extravagance simply by reducing their allowance."

But in the nation's capital, what Reagan called an allowance is more like a necessity. Nearly 19 percent of the District's $1.9 billion budget comes from federal funds, not counting 15 percent more appropriated through the federal payment. Federal spending is woven throughout the fabric of Washington life, and slashing it would have widespread and deep impact.

With fewer federal funds, a city government that has already pruned itself back by laying off 1,600 workers and reducing services from neighborhood recreation centers to hospital care would have to cut sharply or eliminate altogether a number of programs, particularly those that serve low-income District residents city officials say.

Reagan's inaugural day job freeze, if upheld, would have a ripple effect in this company town where the federal government is the company. And those for whom a briefcase and a calling card from a consulting firm are new badges of middle-class status may have their dreams further deferred by the 5 percent reduction in government consulting contracts.

D.C. Mayor Marion Barry was among a group of mayors who met with Reagan last week. Barry said he argued against many of the cuts, particularly youth employment programs. But, Barry said last night, "there are going to be a lot of cuts. I don't agree, but I understand it. Anytime you've got an $80 billion deficit, you've got to do something."

The new administration has not yet announced a definitive list of cutbacks, but specific recommendations by David A. Stockman, Reagan's director of the Office of Management and Budget, would have sharp and immediate consequences:

More than 600 city government workers from low-income families, who now under the Comprehensive Employment and Training Act program perform services that range from supervising playgrounds to filing documents, would lose their jobs, if the CETA program is eliminated, as Stockman has recommended. This is equal to more than a third of the total number of layoffs ordered by Barry last year to ease the city's precarious financial situation.

Another 300 CETA jobs in community-based, nonprofit organizations would be eliminated, in some instances virtually wiping out entire staffs of some agencies. "Some of [the groups] have told us the cuts would be absolutely devastating," said Matthew F. Shannon, an aide to the director of the city's Department of Employment Services.

Hard hit, for example, would be the Washington Area Council on Alcohol and Drug Abuse, which currently operates a 24-hour alcohol and drug abuse telephone hotline solely with eight CETA workers.

"It looks bad," said Mary J. Kidd, executive director of the organization. "We're not really sure of what we're going to do."

A government already struggling to meet the cost of subsidizing health care for low-income residents under the Medicaid program would be faced with an additional $10 million deficit in this area and might have to slash benefits to recipients, according to city welfare officials.

In the District, Medicaid will cost about $170 million this year, with half being paid by the city and the other half coming from the federal government, according to Lee Partridge, special assistant to the director of the city's Department of Human Services.

The additional $10 million burden, Partridge said, would probably necessitate new restrictions on eligibility or benefits. "It's hard to think how we would be able to avoid cutting people or services," she said.

Another area targeted for as-yet-unspecified cutbacks is the Aid to Families with Dependent Children (AFDC) program, which last year helped 85,000 city residents.

AFDC is another half-and-half program, with the city and the federal government each contributing about $46 million last fiscal year. It is also another program whose costs have been rising steeply, contributing significantly to an overall city budget deficit for fiscal 1980 of $105 million.

More than 4,000 District residents qualified this fall for extra unemployment benefits when national unemployment reached an automatic trigger point. Reagan wants to eliminate the trigger, making such extended payments impossible.

A pool of urban development money, now being sought for such projects as the restoration of the Willard Hotel -- an anchor of the plan to revitalize Washington's downtown -- would suddenly dry up if Reagan carries out his reported plans to eliminate the Urban Development Action Grant (UDAG) program.

A 3.7 million grant from this program aided in construction of the new Hechinger Mall at H St. and Bladensburg Rd. NE, which is being touted as a key to the revitalization of the riot-torn H Street corridor.

Another area targeted for cutbacks is energy assistance for the poor and working poor. About 40,000 District residents got help in paying their home heating bills last year, city officials said, with the help of a $5.7 million federal grant. The city also runs, with federal help, a program to help low-income residents weatherize their homes, thus cutting down on fuel costs. This program is also imperiled. t