Fairfax County officials are projecting a budget shortfall of $100 million for the coming fiscal year, and $79 million the following year, because of the lackluster recovery of residential property values and the highest office vacancy rate since 1991.

County Executive Edward L. Long Jr. told a joint meeting of the Fairfax County Board of Supervisors and the School Board on Tuesday that for the seventh consecutive year, the county faces shortfalls that will make it difficult to pay for all the needs that the county has identified.

His projection assumes that property assessments will rise by about 3 percent.

“We’ve cut more than 653 positions” since 2008, Long said. “There’s nothing easy left to cut.”

The effects of the federal government’s sequestration cuts last spring, slow job growth and a weak commercial and residential property market combined to make the budget year look grim. Federal procurement spending, which dropped 12.5 percent last year, is expected to be down 3 to 4 percent this year.

The county is not broke, though. It has two major reserves — one for catastrophes, which contains 2 percent of its $3.72 billion general fund, and the other, often called the “rainy day fund,” which holds 3 percent of the operating budget.

County officials are loath to dip into either fund, in part because bond-rating agencies, whose scores help set the rate at which the county can borrow money, say that Fairfax is on the low end of its peers in terms of how much money it keeps in reserve.

In addition to the projected shortage, School Superintendent Karen Garza predicted that the school system needs $64 million more than the county had planned to budget on its behalf in fiscal 2016, which begins July 1. She pointed to unfunded needs such as lower class sizes, family and early childhood education, better technology, major maintenance needs, bus replacements and the creation of playgrounds compliant with the Americans With Disabilities Act. Garza also said that a pay increase for teachers is sorely needed.

“Frankly, ladies and gentlemen, we are losing our competitive edge,” Garza said, pointing to a salary chart that puts Fairfax’s starting, mid-range and maximum teacher salaries between $2,000 and $16,000 below those in neighboring Arlington County.

Tuesday’s meeting marked the start of several months of negotiations between the schools and the county as they work to create a balanced budget. The Fairfax County executive will propose a budget Feb. 17. After that, the supervisors decide whether to accept or alter it. The property tax rate, now $1.09 per $100 of assessed value, is set when the supervisors adopt a budget.

Board Chairman Sharon Bulova (D) said “it gets harder and harder as time goes on” to find enough local funds to pay for the county’s needs. Garza and others noted that state support for education has not kept up with demand, especially in urban areas such as Fairfax, where student enrollment has increased by nearly 22,000 since 2008, and by almost 3,000 in the past year.

There are 186,785 students enrolled in Fairfax County Public Schools, the nation’s 10th-largest school system.

“We’ll certainly work to avoid raising taxes,” Bulova said. “I’m very much aware of the fact that the residential taxpayer is stressed, and our board needs to be sensitive to that.”