The Prince William Social Services Department is trying to launch a comprehensive effort to help the homeless, even though officials say its budget is already stretched to the limit by the escalating costs of other programs.

The county's first publicly run shelter -- a 30-bed facility on Route 1 in Woodbridge -- is expected to open in mid-July, and social services officials have asked the federal government to allow them to use nine vacant Army apartments in Woodbridge to house homeless families. The Route 1 facility, the site of the old Prince William Motel, will be a full-service center providing food, shelter and mental health and job training services.

The Social Services Department is starting these ambitious programs at a time when the department's budget, which includes state as well as local money, can barely keep up with demand, according to Director Ricardo Perez.

"The economic slowdown {in the Washington area} has really impacted us," he said.

Illustrating the point, the Board of County Supervisors agreed Tuesday to give Perez's department an additional $458,000 in leftover funds from other departments to tide it over until the new fiscal year starts July 1.

The department has had shortfalls in other years, but Perez said rapidly rising needs have made this year's financial woes much more serious. The number of children entering foster care in the county has risen 130 percent this fiscal year, crowding in the Juvenile Detention Home has meant greater staffing needs, and applications for food stamps and Aid to Families With Dependent Children are up more than 25 percent from a year ago, Perez told the supervisors.

The department has instituted a hiring freeze and reduced its general relief program, which financially assists people ineligible for federal aid.

The start of the new fiscal year will ease some of the financial crunch because the supervisors voted to give the department $600,000 more in fiscal 1991 than the $10.8 million it received this year. But Perez said he plans not to fill all 12 vacancies on his staff immediately.

"Rather than . . . having to go back to the board and ask them to bail us out, we're going to start out with a tightened belt," he said. Even with a tighter belt, social services officials are working to expand programs for the homeless. A county task force last year estimated that up to 300 homeless people are in Prince William.

Volunteers have been working since April to renovate the Route 1 shelter, according to county homeless coordinator Betty Matthews, and Volunteers of America, a national nonprofit group, has signed a $240,000 annual contract to run it. Homeless people will be allowed to stay for up to 30 days, said Joseph E. Boro, president of the organization's Washington-area branch.

County officials expect to learn in the next few weeks whether they can also house homeless families in the Army apartments on the grounds of the Harry Diamond Laboratories in Woodbridge, said Deputy County Executive Larry Hughes. Families might stay in an apartment while they worked to accumulate enough money for a security deposit on a rental apartment, Perez said.

"Shelters remove a lot of responsibility from the family -- cooking, for example," Perez said. In the apartments, "we would look at having them prepare their own meals. We would preserve the family and the way it functions."