Fairfax County officials said yesterday that real estate property assessments are likely to rise no more than 2.5 percent next year, good news for homeowners reeling from years of tax increases, but potentially devastating for some government and school system programs.

The announcement on assessments came during a gloomy economic forecast from County Executive J. Hamilton Lambert to the Board of Supervisors. Lambert said the county faces a $60 million potential budget deficit next year, coming at the same time federal funds are declining and the state is cutting local aid because of its own deficit.

To prepare for the worst, the board's budget subcommittee agreed to limit the increase in county funding for schools to 6 percent next year and limit county government spending increases to less than 4 percent. At the same time, the board agreed not to raise property tax rates. A proposal not to raise business taxes faced some opposition and was not decided.

All of the matters will be considered at the board's Aug. 6 meeting.

County School Board Chairman Kohann H. Whitney (Centreville) said that, given existing spending trends, a 6 percent limit on county funding for schools could lead to a $48 million budget deficit. Because personnel costs account for 88 percent of the school budget, she said, "This means people, either how much they're paid or whether they have jobs."

Rick Willis, executive director of the Fairfax Education Association, said, "We're now talking about whether this community gets the school system it demands and deserves, and with these numbers today, I don't see how that can happen."

County spending on schools this year is about $632.2 million. A 6 percent increase would add $37.9 million to next year's spending. Similarly, the county general fund this year is $621.6 million, and holding spending increases to less than 4 percent would mean an overall rise of less than $24.8 million.

"We have got some serious problems we need to address, and the budget guidelines {the limits on spending increases} are going to get at that," said Supervisor Sharon Bulova (D-Annandale), chairman of the board's budget subcommittee. "We don't want to resolve a deficit situation or potential losses with increases in taxes."

For homeowners, the low assessment increase would offer welcome relief from four years of increases that have averaged 15.5 percent. Since 1987, the mean value of a home in Fairfax has risen almost 78 percent, from $109,597 to $194,355 in the fiscal year that began July 1.

With an increase of 2.5 percent, the typical home in Fairfax would increase in value $4,859, from $194,355 this year to $199,214 in fiscal 1992, which begins next July. The tax bill, under the current rate of $1.11 per $100 of assessed value, would increase $54, from $2,157 to $2,211.

That would be the lowest jump in the typical homeowner's tax bill since 1986, when the increase was $18. In the four years since then, the typical bill jumped an average $169.

The assessment increase would be the lowest since 1985, when the mean assessed value on the typical county home rose 1.9 percent over the previous year, from $100,207 to $102,090. Rising assessments similar to Fairfax's have been experienced to lesser degrees by jurisdictions throughout the Washington area, which in the last decade has been one of the country's fastest growing areas. The rising assessments -- and the tax increases they precipitated -- have sparked powerful taxpayer revolts from the District to Montgomery and Howard counties in Maryland to Fairfax.

In response, government officials and politicians in all those jurisdictions are struggling to rein in spending and cut taxes.

In Fairfax, the efforts have met with little success, in part because the government, like local governments across the country, is facing ever diminishing levels of federal and state aid. Fairfax lost about $12 million in state funds this year, and with Virginia's continuing budget crisis, officials say they expect more cuts, possibly as early as next month.

Lambert said he expects Virginia Gov. L. Douglas Wilder to announce that the state, during the next two years, faces a budget deficit between $400 million and $500 million.

State budget officials, saying that changes in tax codes caused them to overestimate tax collections, are dealing with a $151 million shortfall for the fiscal year that ended June 30. Noting the possibility of deeper deficits, they have ordered state agencies to draw up plans for how to cut 1, 3 and 5 percent from their current budgets. Wilder has specifically warned localities that they should plan for additional cuts because about 60 percent of state funds gets passed back to them.

Lambert said the county's projected $60 million deficit in 1992 does not account for the possibility of deeper cuts in state funds.

He said the state could withhold $16.5 million in recordation tax revenue the county expects to receive during the next two years. Furthermore, Lambert warned that a state commission studying the inequity of education funding throughout the commonwealth may recommend changes in how sales taxes are distributed to localities. Such changes could cut $21 million in state aid to county schools.

Board Chairman Audrey Moore (D) first raised the alarm about next year's potential budget deficit in a speech two weeks ago. She said again yesterday it may be necessary for the county to cut the current budget to account for lost state aid.

Bulova said that if revenue picks up, the county and school system "will be sharing a brighter picture. In the same vein, if things get worse, we'll all sit down and share the misery together."