Alexandria, a city of 103,000 residents, will have to operate with about $2.8 million less in federal funds than it had last year, and this reduction will trim local programs in social services, education, health and public works.

By 1984, said Alexandria Mayor Charles E. Beatley Jr., the city will really start to feel pressure from the loss of federal dollars. "They don't realize what's going to happen to them," said Beatley, a Democrat, referring to the city's poor, who will suffer from cuts in food stamps, job training, health services and other aid programs.

The city will absorb social service cuts of $352,000 this year, officials said. Local poverty programs are still operating under previously allocated funds, but City Manager Douglas Harmon called this period "the rough interlude before the bigger storm hits . . . . The pipeline hasn't dried up even though the spigot has been turned off."

Alexandria officials are concerned that cities will fare poorly when it is left to the state to divide federal block grants. The city is losing population and, hence, the voting clout to fight for its interests in the General Assembly.

Republican Vice Mayor Robert Calhoun said programs like food stamps, CETA and Aid to Families with Dependent Children are not the type of services localities should pay for if the federal government isn't going to fund them.

He is more sympathetic to local funding for what he calls "traditional" welfare and public health assistance for the poor, worrying that Alexandria could end up paying more for these kinds of programs. He said one of the threatened programs, companion service for the elderly, now costs the city $100,000. Without financial help from that program, some elderly might have to go into a nursing home at a possible public cost of $15,000 to $30,000 each per year.

The city has set aside $400,000 to help make up for federal cuts in social services such as these, said Calhoun. "But we're going to have to pick our shots," he added. He said he hopes federal cuts don't fall only on the poor, and he believes local Republican officials like himself should not go out on a limb to support the President's programs.

"We're trying to run a city irrespective of political affiliations and to the extent that the federal programs help us, that's wonderful," he said. "But we should be prepared to criticize them when they don't."