Fairfax County, under fire from parents whose children are not eligible for county-run day care programs, is considering a policy shift that would open the county's 52 school-based day care centers to children on a first-come, first-served basis.

Currently, only the pupils who attend the public elementary schools in Fairfax County where the day care centers are based may enroll in them. Private and parochial school pupils, as well as pupils at the 64 elementary schools that have no day care facilities, are not eligible for county-run day care for school-aged children.

The proposal, which the county Board of Supervisors is scheduled to consider at its meeting today, is a further sign of the day care crisis that has gripped Fairfax County as elementary school enrollment climbs and more mothers enter the work force.

There are 1,724 pupils enrolled in the county-run centers, which offer before- and after-school day care. County officials estimated last fall that another 2,827 public elementary school pupils need day care facilities.

The officials say they do not know how many additional private school and parochial school children would take advantage of the program, if it were open to them.

If the county supervisors decide to open the day care centers to all school-aged children, it is unlikely there would be an accompanying increase in the number of pupils the centers could accommodate, according to county officials.

Rather, parents would be able to apply for the same number of day care slots, and the county would have to devise some form of first-come, first-served policy of selecting the children.

Parents whose children are enrolled in county-run day care centers pay a fee that is based on their income.

Supervisors are split on changing the county board's policy on day care center enrollment. Any change in policy would have to be ratified by the county School Board.

The county's public schools started offering child care services before and after regular school hours in 1975. Since then, the county has expanded the program to include day care centers at more schools nearly every year.

However, rising elementary school enrollment has put available free space in the schools at a premium, and county officials say there is little chance of adding more day care centers at the elementary schools in the near future.

"The situation with respect to space in public schools is critical," said Verdia L. Haywood, deputy county executive for human services. "It will be extremely difficult to expand [the current program] in any significant manner."

In March, the county board asked its staff to seek more day care services with the help of private businesses in the county.