The Carter administration's budget-balancing act may dash Fairfax County school officials' hopes for restoration of $9.9 million in federal impact aid, which was slashed from the Carter budget earlier this year.

To Fairfax taxpayers, the national belt-tightening may mean that the $9.9 million -- money already included in the revenue column of the county's proposed $347 million school budget -- will never materialize.

"Every year we've had an uphill fight and the budget is even more difficult this year," said Rep. Joseph Fisher (D-10th District), a leading proponent of the federal aid program. Fisher will testify this week before the House Appropriations Subcommittee on Labor, Health, Education and Welfare in favor of restoring the federal schools subsidy.

Since its inception in 1950, impact aid has been an annual target of thrifty congressmen, but the funds have usually been restored at the last minute. Carter's anti-inflation speech last week, calling for an additional $13 billion in budget cuts, left school officials with little hope of regaining the money this time.

"We certainly didn't find anything to be encouraged about," said Fairfax County school budget director Myron Cale in reaction to the president's speech.

For beleaguered Fairfax County school officials, such a loss of federal aid could come as the second blow to school finances. Gov. John N. Dalton's budget left the Fairfax schools $7 million short of what they expected in state aid. The school board has asked the county to make up the loss. If the county agrees, it will result in a 4-cent increase in the county property tax rate, according to acting county executive J. Hamilton Lambert.

At a press conference last week, school board chairman Rodney F. Page accused Dalton of ignoring state board of education requests for an increase in state financial support of education. He also blamed Dalton for the potential increase in county real estate taxes.

School officials have said that if the federal dollars are not forthcoming they will again ask the county to make up the funds. But taxpayers may not want to subsidize the impact-aid students, school officials said.

"Without federal impact-aid money, the county taxpayer will be paying for the education of students from Ft. Belvoir, whose parents live and work on federal government property," Cale said last week. "They don't pay county property taxes and, let's face it -- military people are able to shop at the commissary and, therefore, even less of their money comes into the county."

Making up the $9.9 million in impact aid, according to county officials, would not be a simple matter, even if county board members wanted to do so. Because of the timing, the funds could not immediately come from higher taxes.

"The problem is that the county has already advertised a 4-cent tax increase . . . and by law cannot raise taxes any higher (if asked to replace the $9.9 million in federal aid)," said one official.

The impact-aid program was enacted after World War II to compensate school districts for the cost of educating children whose parents either live or work (or both) on federal property. School operating funds, for the most part, come from the property taxes paid by homeowners and businesses. When the parents of school children live on federal property and work for the government -- as is the case with families at Fort Belvoir -- no property tax revenue is generated.

The program has been criticized on the grounds that funds often have gone to the affluent Washington suburbs where most government workers do not live on federal property and already pay high property taxes.

According to school records, Fairfax County has 1,630 federal impact-aid students.

In January, Carter called for the elimination of impact aid to school districts where the funds comprise only a small percentage of the school district's revenues.

"This is going to be a bloody battle," predicted budget director Cale. "We are in dire danger of losing all of that money."

A staff member of the House appropriations subcommittee, which will act on the impact-aid question, said earlier this week, "We believe in doing things gradually. I don't think this committee is going to be irresponsible by whacking everything. I do believe some of the funds will be put back into the budget."