Mayor Sharon Pratt Dixon's slash of the District budget yesterday was, at first blush, a far piece from what is unfolding this month at 4909 First St. NE. There, the renovation of a two-story brick building is nearly complete, and the four low-income families who have long been tenants soon will move back home.

Except they hope to be going home as owners of their units, not renters. And the key to their dream is something called the Home Purchase Assistance Program, which is supposed to turn over $115,000 to close the deal, said Jim Dickerson, co-director of Manna, a nonprofit organization that helps low-income residents with housing.

That program, though, is operated by the District's Department of Housing and Community Development. And Dixon ordered that department to cut its fiscal 1991 budget nearly in half.

No one knows yet what that means for the project at 4909 First St. But it is a small example of what is at stake in the massive reductions announced by Dixon in an effort to contain the District's budgetary deterioration.

Among the hardest hit were four agencies involved in housing, development and jobs: the Office of Business and Economic Development, whose budget was cut 45 percent; the Department of Employment Services, 40.5 percent; the Department of Public and Assisted Housing, nearly 12 percent; and the Department of Housing and Community Development, 45 percent.

Officials of the agencies declined to identify what they would eliminate to comply with Dixon's mandate, saying they are reviewing budgets. Many positions in the four agencies already are vacant, and could be cut without further effect on employees or services. In the Department of Housing and Community Development, 88 of 403 positions -- nearly one out of five -- were unfilled as of a year ago.

In addition, a commission headed by Alice M. Rivlin, former director of the Congressional Budget Office, said in its recent analysis of D.C. government that there are 168 unnecessary management positions in the four agencies. The commission also complained that the District has too many agencies working in housing and development.

But several community activists said yesterday that so much has to be cut to meet Dixon's goals that programs would seem to be in jeopardy, even after any cost-saving recommendations made by the Rivlin Commission are enacted.

While stressing he is unaware of what the Department of Housing and Community Development might cut, Dickerson said the 45 percent reduction overall is "going to mean disaster."

Through a variety of programs, the department helps residents and organizations renovate and purchase housing, and Dickerson said the District already is unable to fund $4 million in projects "that are ready to go to tenants that the department committed to last year."

"It's another shocker," he said of Dixon's cuts. "We have very, very serious problems facing us in regard to affordable housing."

Alice Vetter, executive director of another nonprofit group that helps residents with low-income housing, said that because she served on the Rivlin Commission, she has come to believe there is "a little bit of give" in the budgets of most District agencies. Beyond that, the District receives substantial amounts of money for housing from the federal government.

Even so, Vetter added, "45 percent is a big number."

Vetter, who heads a group called Ministries United to Support Community Life Endeavors, said any cuts in the Housing Purchase Assistance Program "would affect what we're doing a great deal. We really depend on HPAP."

Brenda Strong Nixon said she feared for the District's $6.1 million Summer Jobs for Youth program, which is operated by the Department of Employment Services and is designed to provide work and training for any city youngster who wants it.

"There is great fear that in order to meet the marks given to the agencies that nothing is going to be left untouched, except those programs under court order," said Nixon, executive director of Associates for Renewal in Education, which received a $1.2 million contract last summer to provide jobs for 3,500 youngsters.

Nixon added, though, that because the programs are so valuable, "I find it hard to believe that she {Dixon} is doing this."