With its day-care program for poor children in jeopardy because of state cuts, Prince William County has won a temporary reprieve that will extend services through December, but county officials warn that without more money, the program will close Dec. 31.

"It's a stay of execution," said Kathy Pierce, fiscal officer for the county's Department of Social Services. "A lot of these people are living on the edge anyway, and now they don't know from month to month whether they're going to have day care for their children."

Prince William is one of dozens of counties in Virginia whose subsidies for day care were cut by state officials this fiscal year--shortfalls that came just a year after the state gave localities extra money to expand their programs. With more than $3 million in day-care support last year, the county had expanded its program from 550 to 800 children. But this year the state slashed that $3 million to $1.2 million.

Arlington, Fairfax and Loudoun counties and Alexandria also suffered cutbacks in subsidies this year--some by half. The so-called "fee" day-care program is a sliding-scale system that helps keep working parents at work. Many clients have been recently forced from welfare rolls.

A crisis has loomed since October in Prince William, which has less local money to make up for the state cuts. Prince William officials sent letters to 300 families telling them the program would close yesterday. The county put up $300,000 in local money to fund the program through November, and the state Department of Social Services recently gave Prince William an additional $250,000 to tide the families through December. The county sent out another round of letters explaining the reprieve.

But so far, Virginia has offered no longer-term solution. State Social Services Commissioner Clarence H. Carter said in October that he was trying to find short- and long-term money to continue the increased subsidies to localities. But no more money has surfaced. A spokeswoman for Carter, Lenora Hardy, said yesterday that "nothing has changed."

The state had encouraged Prince William and other Northern Virginia localities to expand their day-care programs. But as welfare reform has spread across Virginia, demand for child-care subsidies has grown, and the state money was spread more thinly this year.

Meanwhile, waiting lists for day care have begun to balloon across Northern Virginia. Nearly 600 children are on the list in Prince William, Pierce said. Alexandria, whose subsidy was also increased and then cut, now has no place for 1,000 children.

"There have been days when I get 40 calls in a day from families that are just eking by," said Elizabeth Henry, Alexandria's day-care coordinator.