Students listen to teacher Heather Ulsh during a reading exercise at Lynbrook Elementary School in June 2014. (Photo by Astrid Riecken For The Washington Post)

Fairfax County school officials have been sounding the alarm about a potentially significant budget shortfall that could lead to major cuts next school year, with the most recent estimates forecasting the deficit at the state’s largest school system at $71.6 million.

Budget officials presented the estimates to school board members on Monday during a day-long work session but warned that the numbers are preliminary and that the situation is fluid. The potential shortfall means that the school system, one of the nation’s largest, will have to seriously consider a number of proposals to balance the budget, including cuts to popular programs.

A citizen task force has begun to examine where those cuts could occur, and a suggestion to get rid of all high school sports already has raised the ire of community members. Other suggested cuts could come from raising class sizes, cutting full-day kindergarten or reducing the number of classes high school students would take, which would narrow the number of electives for each student.

[Read more: Could one of the nation’s largest school districts go without sports, activities?]

“We will have some kind of significant deficit,” Superintendent Karen Garza said. “What that number is is still yet to be determined.”

Assistant superintendent Kristin Michael told board members Monday that the district “continues to face fiscal challenges,” but warned that the numbers she presented could shift.

The district has said the shortfall could range anywhere from $50 million to $100 million depending on a number of factors outside of school system’s control. They include how much aid will come from the state and how much county revenue the district will receive. The latter is a perennial source of tension between the school system and the county government.

[Viewpoint: Can one of the nation’s top school systems ‘keep the promise’?]

The district has sought input from the community, urging them to try out an online budget tool that allows them to suggest cuts. The district will offer another budget estimate in November and Garza will present a proposed budget in January.

[Read more: Building a school budget? There’s an app for that.]