Prince William County’s schools enrollment boom has outpaced the growth of the district’s budget for years, a quandary exacerbated by the recession. Class sizes have ballooned. Bus service has been cut. Per-pupil spending has flattened.

Faced with the prospect of the county’s enacting a smaller than planned increase in the property tax rate, the school board has again begun weighing drastic cuts, this time to the district’s treasured universal full-day kindergarten program, which Superintendent Steven L. Walts once touted as his “greatest accomplishment.” After years of cutbacks, board members said there are few places left to look to save money.

“It’s more of an economic calculation than an educational calculation,” said school board Chairman Milton C. Johns (At Large), who has championed the expansion of the program. “We’re out of options.”

The debate over whether to keep the program in the face of budget constraints is taking place while Loudoun County, one of few districts in Virginia that do not have universal full-day kindergarten, continues to weigh whether such a program would have value for students not considered “at risk,” a grouping that includes those in poverty. Similar scenarios are playing out across the country, with broader support for full-day classes running up against tightening school budgets.

One proposal in Prince William would eliminate full-day kindergarten classes at more than half of the 57 elementary schools, affecting thousands of youngsters.

Johns said the district allowed class sizes to grow to deal with funding cutbacks. But class sizes are approaching the legal limit, and the district aims to reverse the trend, he said.

Johns and other board members have started to look at cost savings that could be achieved by eliminating programs not required by state law. The district is obligated only to provide a half-day of kindergarten, although nearly every district in the state offers full-day kindergarten to all youngsters.

“From an instructional perspective, yes, we think full-day kindergarten is absolutely needed,” said Dave Cline, associate superintendent for finance and support services. “But somewhere along the line, we’re going to have to continue to make more and more difficult choices.”

The Prince William Board of County Supervisors signaled in mid-December that it would increase the residential tax rate by 1.3 percent instead of the 4 percent that had been outlined in a five-year plan. If the board follows through with the 1.3 percent increase, schools would get an increase of only $12 million over this year’s budget instead of the $24 million they had anticipated. The county gave $487 million to the school district this fiscal year.

Corey A. Stewart, the chairman of the Board of County Supervisors, said the move to alter the tax-rate increase was only a proposal to force the schools to make savings. He expected that, ultimately, the tax rate would not fall that far. He said he would not support a school budget that eliminated universal full-day kindergarten.

At the same time, it was unclear whether the county supervisors could restore enough revenue for the district to afford to keep full-day kindergarten.

A meeting of the school board is scheduled for Feb. 4, when members will continue budget discussions.