Acting Fairfax County Executive Richard A. King, saying there may not be enough revenue to pay all of the county's bills, ordered his staff directors yesterday to plan a possible 5 percent cut in spending for the rest of this fiscal year.

King also asked department heads to prepare to cut next year's spending levels by a total of 10 percent from the current budget, which runs through June 30. That is twice as great a reduction as was requested just months ago.

King said it was impossible to determine the exact dollar total of the cuts being considered, although it could reach millions. The county already is trying to find $10 million in cuts this year to resolve a lingering deficit, and officials said that figure could grow if tax collections continue to lag.

If the cuts are implemented, they could range from delaying building projects to paring supervisors' office budgets, officials said.

"The bottom line is this is very serious," said Sharon Bulova (D-Annandale), chairman of the Board of Supervisors budget committee. "I think you're going to see some very difficult things being done. We're keeping very close tabs on our revenues that are coming in."

"It is a management initiative which I consider to be prudent on our part to at least examine our fiscal situation in light of the current recession and the activities occurring in the {Persian} Gulf," said King, who became acting county executive this month.

"We have to assess each of these agencies and see what a 5 percent reduction would do. In some agencies, there may be funds available which could be used if needed."

The cuts would come from the county's $630 million general fund and probably would not affect the transfer of county funds to the school district, board officials said yesterday. The schools this year found $19.3 million in surplus funds that will carry them through next year.

Fairfax's situation is consistent with the gloomy economic forecasts for the entire area.

Prince George's County Executive Parris N. Glendening has laid off 190 workers and frozen 649 vacancies to deal with a $50 million shortfall. Montgomery is projecting a $100 million deficit next year.

District officials ended fiscal 1990 in September with a $93 million deficit, and they expect a shortfall as high as $300 million this year.

Fairfax supervisors received a glimpse of things to come at a gloomy midyear budget session on Monday. At that meeting, supervisors were told that there was a $24 million drop in property taxes compared with last year.

King's actions are a continuation of cuts made last year by his predecessor, J. Hamilton Lambert. Until now, the county had sought to close this year's deficit by leaving 867 positions vacant, reducing travel and overtime, delaying purchase of new equipment and reducing the printing of county publications.

Lambert also stopped giving cost-of-living increases to the county's 30,000 school and government employees.

Locally, a slump in real estate values has led to a projected flattening in property assessments. Those assessments had soared in recent years, funneling millions in property tax revenue into local government coffers.

With holiday sales receipts still undetermined, county budget officials are reacting to the possibility that income may continue to decline.

"The likelihood is that we will need the reductions," said Board Chairman Audrey Moore (D). "It's important and a test of our ability to govern in lean times."

Tax revenue from new development is projected to rise 2 percent this year, the smallest rate of growth in Fairfax County in the post-World War II era.

The number of home sales in the county in the first 10 months of 1990 was 28.4 percent lower than in the first 10 months of 1989, and the number of building permits issued from July to September was down 31.6 percent from the same time in 1989.