The Fairfax County Board of Supervisors approved a spending plan Tuesday that includes tax increases, raises for county employees, more money for schools, and higher sewer fees and fees for adopting pets.

The supervisors voted 7 to 3 in favor of a $3.7 billion budget proposal for fiscal 2015, and they are scheduled to formally adopt it later this month.

The proposal would increase the average real estate tax bill for a Fairfax homeowner by $357 next year after supervisors approved a half-cent increase above the rate for fiscal for 2014. The overall budget would increase spending by 3.3 percent from what was approved for this fiscal year.

Board Chairman Sharon Bulova (D) announced that a task force will study bringing to a referendum a possible countywide meals tax as part of an effort to diversify the revenue stream. The effort will be led by former secretary of the commonwealth Katherine K. Hanley and former congressman Tom Davis (R-Va.), both of whom have chaired the Board of Supervisors.

Supervisor Pat Herrity (R-Springfield) expressed concern about burdening county residents with more taxes.

“There is something fundamentally wrong when Arlington County can cut a whole penny off of their tax rate but Fairfax County cannot,” said Herrity, who voted against the budget proposal. He said the proposed real estate tax rate of $1.09 per $100 in assessed value would contribute to a 14 percent increase in three years. The proposed meals tax adds “insult to injury,” he said.

The budget would have county government provide $1.7 billion in local tax dollars for the school system operating budget, an increase of $51.5 million, or 3 percent. School officials were initially told to expect a 2 percent increase, and several supervisors cited the additional 1 percent increase as evidence that the school system is their top priority. The school system relies on the county for about 70 percent of its $2.5 billion budget.

But School Superintendent Karen Garza said she was disappointed that supervisors did not meet her request for a 5.7 percent increase, or $98.1 million more than the county gave the school system for this fiscal year.

“It’s unfortunate and sad that clearly we are not the priority,” Garza said. “The numbers reflect that.”

Garza said the Board of Supervisors’ action means that pay increases for teachers and other employees in the coming year will probably not be as generous as she had proposed. She said some employees might not receive any pay raise.

Garza said that class sizes probably will increase — as she had proposed in her spending plan— but that the increase would not be greater as a result of the supervisors’ funding proposal. “We’re asking our employees to do more with less,” she said. “It’s demoralizing.”

School Board Chairman Ilryong Moon (At Large) said the original school budget called for $96.5 million in cuts — including a reduction of 732 staff positions — in response to a projected shortfall. He said the school system would now have to address an additional shortfall of $47 million, resulting in the elimination of 250 to 300 more positions, under the supervisors’ spending plan.

In all, as many as 1,000 of the school system’s 22,000 employees might be cut, a loss of about 4.5 percent. Garza has said that the reductions would be made through attrition and possible layoffs.

“We are at a tipping point,” Moon said. “It’s going to really hurt us.”

Bulova said the school system shortfall might be alleviated by $30 million in projected state funding that has not been approved because of a standoff at the state Capitol in Richmond. The supervisors also advised school officials to plan for a 3 percent increase in county funding in fiscal 2016.

Under the proposed fiscal 2015 budget, most county employees would receive a 2.3 percent pay raise. Bulova said public safety workers, including police officers and fire and rescue personnel, would receive step salary increases.

The budget calls for the rate for sewer service to increase by 7 cents, to $6.62 per 1,000 gallons, and the base charge to rise to $15.86 from $12.79 per quarter.

Pet-adoption fees charged at the county animal shelter could increase by more than 300 percent for dogs and cats. The fees are now $40 for dogs and $30 for cats. The budget calls for a fee schedule that takes into account a pet’s age, ranging from $100 to $175 for dogs and from $50 to $125 for cats.