Fairfax County is having the kind of problem the deficit-ridden federal government would love to see: a budgetary surplus. So strong is the county's financial position that local politicians are considering a tax cut for the fiscal year starting July 1.

When the county Board of Supervisors meets today to consider its financial position midway through the fiscal year, supervisors will review a budget that features a projected "available balance" of $15.5 million that the county has not committed.

County Executive J. Hamilton Lambert has presented the board with a little more than $8 million in possible midyear expenses; but even if all of them are adopted, that will leave a projected surplus of $7.4 million for the wealthy suburban county.

The county's healthy financial position has led to predictable talk by local politicians of both parties of a tax cut in fiscal 1986.

"We're in a position, I think, to . . . reduce taxes for the citizens of Fairfax County and still keep the county in excellent financial condition," said Supervisor Joseph Alexander (D-Lee). He said, however, that the board would have to grapple with the question of whether to reduce real estate taxes, personal property taxes, or both, and by how much.

Supervisor Thomas M. Davis III (R-Mason) also raised the possibility of a tax cut when the board formulates the fiscal 1986 budget this spring.

In a memorandum last month to the board, Lambert attributed Fairfax's comfortable financial position to increased county taxes generated by a burgeoning local economy, including more sales, business gross receipts and housing starts.

Most of the $8 million in programs the board is slated to decide on today are one-time costs. Among the items the board is likely to approve is a $405,000 expense to address the problem of child abuse through the police department and the department of social services; $1.6 million for worker's compensation claims; $775,000 for renovations to the Massey Building, the county government's headquarters, and a variety of minor repair and construction projects.

The board also will mull a $100,000 contribution to Wolf Trap Farm Park, the performing arts center in the county. Lambert included the item as a matter for the board's consideration, but he did not recommend it for approval. Davis, citing more pressing needs in the county -- including low-cost housing for the poor -- said he would oppose the contribution to Wolf Trap.