Fairfax County Schools Superintendent Karen Garza announces her proposed budget at West Potomac High School on Jan. 7, 2016. (Donnie Biggs/Fairfax County Public Schools)

Fairfax County Executive Edward L. Long Jr. is recommending a tax increase for homeowners that would average $304 a year to cover a projected budget gap of about $93 million for the 2017 fiscal year.

The proposed increase — equal to about 4 cents per $100 of assessed value — was met with dismay by some supervisors and would fall about $68 million short of what Fairfax school officials are seeking in the budget, which probably means another bitter year of spending negotiations in Virginia’s largest county.

“It’s a pretty dark and dreary and ugly day,” Supervisor John C. Cook (R-Braddock) said Tuesday after Long finished his budget presentation to the County Board of Supervisors. “Four pennies is not something I can swallow. I think it’s going to be very difficult.”

In Long’s presentation of a proposed $3.99 billion general-fund budget, he described a host of fiscal challenges Fairfax faces in the coming year.

The lingering effects of federal spending cuts have kept commercial tax revenue stagnant and prevented the county’s home real estate market from rebounding as strongly as elsewhere in the country, Long said.

Meanwhile, the county school system is struggling to fund more English-instruction courses and more free-and-reduced lunches for a steadily growing population of 187,000 students that includes growing numbers of poor and immigrant children.

Local roads, parks and county buildings are worn, and pressure is mounting to begin implementing $35 million in changes to the county police department that were recommended by a specially appointed police commission.

In short, Long said, Fairfax is hurting for extra tax revenue.

“At the current real estate tax rate, revenue growth has been insufficient to fund all of our priorities,” Long said.

A 3-cent rise in the current residential tax rate of $1.09 per $100 of assessed value would only meet minimum spending requirements that do not include some crucial needs. Among them: long-term economic-development projects and investing in technology to keep county computers safe from hackers.

Long said that a 4-cent increase in the tax rate would allow the Board of Supervisors flexibility to allocate more funds to schools or other programs.

On March 1, the board will decide a cap for the 2017 tax rate, although it could choose to formally adopt a lower rate in April.

“That’ll be the big debate in the next couple of weeks. . . . What tax rate do we advertise?” Long said at a news conference after his presentation. He said that every penny increase in homeowner taxes raises about $23 million more for the county.

If the Board of Supervisors approves Long’s recommendation to increase the tax rate by 4 cents, it would be the largest such increase since 2010, when it approved a 12-cent hike to combat the effects of the 2008 recession.

On Tuesday, county school officials argued that the $68 million shortfall in funding proposed by Long would lead to classroom cuts and make it harder to raise teacher salaries.

A group of teachers and board members rallied outside the government center to push for more funding.

“Unless the Board of Supervisors provides for a funding increase above Mr. Long’s recommendation, Fairfax County Public Schools will once again have to make damaging budget cuts that will reduce educational opportunities for our children,” Pat Hynes, chairman of the School Board, said before the rally.

Supervisor Pat Herrity (R-Springfield) argued that the county should be looking for more cuts, particularly in the county’s pension spending, before raising homeowners’ tax rate.

“It is past time to make tough decisions,” Herrity said.

Supervisor Penelope A. Gross (D-Mason) contended that Long is right to recommend spending about $1 million on improving county trails, athletic fields, pedestrian bridges and parks facilities.

“We’re fraying at the edges,” Gross said. “We’ve got things that are looking shabby, and that are shabby.”