Fairfax County school board members and county supervisors set the stage for a political showdown over next year's proposed school budget after supervisors warned the board yesterday that its request for a 10 percent spending increase is "totally out of line."

"We're going to have a difficult time defending this much of an increase in the school budget with a declining student population and the pressure to consolidate schools," Supervisor Joseph Alexander told school officials during a tense breakfast meeting. "It's not just the dollars--we're looking at public pressure."

School board members, however, said they would not trim their $432.9 million budget and told supervisors that if they want the budget cut they should exercise their authority to reduce the budget themselves. Under state law the supervisors can set the total amount of the budget but have no legal control over how the money is spent.

"I don't see where there can be further cuts," said school board Chairman Ann P. Kahn. "We have a responsibility to reflect the needs of education in this county."

Kahn said the board had already reduced the superintendent's proposed budget by $2.3 million before it was sent on to the supervisors. That was only the second time in 10 years the school board had cut a superintendent's recommendation.

"The expenditure increase is totally out of line with the county and other local school systems," said Board Chairman John F. Herrity. He noted that the county has set a 6.1 percent limit on its own spending increases, the smallest raise in recent county history.

In contrast, Herrity said, the school board's request outdistances the year's inflation pace and is the largest budget increase requested by any suburban school system in the metropolitan area.

While yesterday's informal meeting over scrambled eggs and fresh strawberries had been planned as a negotiating session by the school board, it ended with the two sides forcing each other into tight political corners. It was the first time in recent years that the school board asked supervisors to discuss budget problems before the document was officially presented to the supervisors for a public hearing.

Supervisors warned the board repeatedly that it should trim its budget before the supervisors begin public hearings on it April 12, but stopped short of telling the board how much to cut.

"We would like it if you would address the cuts rather than forcing us into making untenable decisions," said supervisor Sandra L. Duckworth. " . . . We are very concerned about what appears to be runaway administrative costs and projected new programs."

Some school board members agreed the school budget is too high. But when it comes to actual cuts, said school board member Toni M. Carney, "I don't think anybody likes to be the bad guy."

School board members said an unexpected appropriation from the General Assembly would reduce the county's $288.6 million share of the budget by $3-4 million. Supervisors said they would not consider that a budget cut because the board would be spending the same amount of money overall.