Even before the Acting Fairfax County Executive J. Hamilton Lambert explained his proposed 1981 county budget and its accompanying boost in real estate taxers at a press conference earlier this week, a diagram in the corner of the room told most of the story.

Perched on a wooden easel was a drawing of a financial pie showing that 48.7 percent of all county spending next year would be for schools.

Lambert emphasized at the outset of the meeting, that inclusion of the $217 million school board budget request -- an increase of $37 million in county funds over the current year -- in his budget, was not evidence of support for the plan, but a requirement under state law."

"I am bound by law to transmit the school budget (to the supervisors) as I receive it," Lambert said. "The supervisors can change by major category or lump sum, as they choose."

Follwoing a series of public hearings during the first week in April, the County Board will make revsions in the budget and approve the final version on April 28.

In a message to the press, Lambert explained that an increase in school spending was the sole reason for the proposed tax rate increase of 4 cents per $100 of assessed value.

Hamilton said that when he prepared the budget in early January, "I had balanced the general fund with projected revenues using the school board's advertised budget figures."

However, the school board's final proposal included a request for an additional $7.1 million, Hamilton noted, forcing him to recommend a tax rate increase.

A reduction in anticipated state funds was the primary reason school officials last month asked for the additional $7.1 million in county funds. Despite the tax hike that would be needed to fund the request, school officials maintain their budget proposal is a "realistic" one.

Since early January, when the school budget was announced, administrators have been hit with a series of unpleasant surprises.

First came Gov. John N. Dalton's "austere" state budget proposal, which left the school board with a $10.5 million shortfall in the 1981 budget. Based on that projection, school officials immediately requested the extra $7.1 million in county funds. (Dalton's $11.5 billion proposal for 1980-82 has been approved with minor changes by the House of Delegates and has gone to the Senate for consideration.)

Then came a new set of recommendations by President Carter concerning federal impact aid.

"For the first time in my 11 years (with the county schools), we have a strong threat of losing every cent of federal impact aid," said school budget director, Myron Cale. "I am becoming concerned."

Cale said county schools were scheduled to receive $9.9 million in federal impact aid next year -- before the new guidelines.

"We are struggling with this budget now," Cale said. "How we could lose another $10 million is beyond me."

To make matters worse, Cale says the decision on impact aid may be put off until next fall, well into the county's fiscal year, making plans at this time useless.

School administrators, however, are not taking the financial beating laying down. They have appointed a liaison to plead their case in Richmond and have a representative on the Virginia Commission for Fairer Impact Aid Money.

Officials also say they are investigating the possibility of legal action against the state and federal government to force more funding for education.

"At this point that's all it is -- an investigation," said Jay Jacobs, school system's liaison in Richmond.

On the average, Jacobs says he spends two or three days a week in the Capitol, letting legislators know that Fairfax County is not satisfied with the governor's budget and that the county expects the legislature to make some additions for education.

Jacobs says he is encouraged by the House Appropriations Committee's decision to allocate an additional $32 million to education.

"The budget is now over in the Senate," Jacobs said. "The Senate can do anything with it. My own opinion is that I doubt they will cut off any of the funds from education, but I don't think the prognosis for a lot more money is too good either."

County educators are launching a campaign that they say will let the County Board know that the voters are interested in quality education and are willing to pay for it.

Fairfax Education Association (FEA) President Gerry Gripper says he is meeting with each County Board member personally to ask for passage of the school board's budget. In addition, the 6,500 FEA members will be distributing leaflets with a tear-off postcard to mail to the board urging support for the budget.

"Most of our energies as an organization are being channeled into gaining support for the school board's budget," Gripper admits. c

Across the county, PTA members are being asked to testify at public hearings and write letters to supervisors, according to Toni McMahon, president of the county Council of PTAs.

"We have 151 units in the county and each is being asked to send a speaker to the public hearings," McMahon says.

According to the county clerk's office, the movement is having an effect, with an unprecedented 45 speakers already assured of a place at the podium during budget hearings scheduled for April 7, 8 and 9.

"We're at the bottom of the barrel in public education," lamented school budget director Cale. "We can't set the tax rate, all we can do is ask the supervisors for the necessary funds."