Correction: Earlier versions of this story misspelled the last name of Kilmer Middle School parent Kim Farrell.

Fairfax County’s class sizes could balloon, teachers could face layoffs and parents might have to pay new testing fees next year under a budget Schools Superintendent Karen Garza unveiled Thursday. The proposal includes $96 million in cuts that would eliminate about 730 staff positions from Virginia’s largest school system.

Garza, who came to Fairfax County in July, inherited an administration facing a dire fiscal outlook for 2015, with a $130 million projected budget shortfall. In her first significant proposal as superintendent, Garza called for a $2.5 billion plan that, despite proposed cuts, represents an overall increase from last year’s budget.

The proposal includes cutting the number of assistant principals and removing about 460 classroom positions in county schools. It also would increase class sizes from kindergarten through 12th grade and pass $4.2 million in testing fees for Advanced Placement and International Baccalaureate classes on to families.

But Garza also proposed $41 million in raises for 95 percent of the system’s 23,000 employees, a move she said is necessary to curtail an exodus of teaching talent to surrounding jurisdictions. Fairfax’s pay lags behind that of several neighbors in the region.

“We have been presented with a daunting task,” Garza said. “We are keenly aware of the effect these cuts will have on our system.”

Garza’s proposal begins what has become an annual showdown between the School Board and the Board of Supervisors, which sends taxpayer money to the schools. The boards have clashed in recent years, with School Board members arguing that funding has not kept up with the school system’s growth and supervisors countering that the system has failed to live within its means.

This year appears to be no different. Garza is requesting a 5.7 percent increase in the county transfer, the equivalent of about $98 million in extra funds. That’s about $60 million more than supervisors have repeatedly said they’re willing to give the School Board. Last year, the supervisors told the schools to expect a 2 percent transfer increase, worth about $33 million in additional funds.

Supervisor John C. Cook (R-Braddock) described Garza’s proposed budget as business as usual, with an unrealistic request that’s unlikely to be met.

“I understand the schools are pressed financially. So is the county,” Cook said. “I don’t think you’re going to see a transfer at that percentage. . . . Taxpayers are being stretched.”

Garza said that the 2 percent increase supervisors have promised will not meet the schools’ needs. “We are calling upon our county leadership — we need their support now,” Garza said, noting that if the request is not met, the schools’ fiscal position “will be much, much worse.”

Jane K. Strauss (Dranesville), who is one of the School Board’s longest-serving members, described Garza’s proposal as a reality check — an “OMG budget.”

Strauss said that if the supervisors decide to provide the schools with less than Garza is requesting, more employee positions might be cut and class-size increases could be higher. “There’s no more low-hanging fruit” to cut, Strauss said. “At the local level, we can’t continue to tout the quality of our schools and not fund them.”

Staff cuts and increased class size are controversial proposals in a county that prides itself on its school system, and parents immediately had negative reactions. Garza’s proposal calls for class sizes in elementary and middle schools to increase by half a student, on average, and high school class sizes to rise by one student.

Kim Ferrell, who has two children at Kilmer Middle School in Vienna, said increasing class sizes will adversely affect students’ education. In some areas of the county, she said, elementary schools already have more than 30 students per class.

“The thing is, we have class sizes in certain schools that are not sustainable, and it hurts teachers and it hurts children,” Ferrell said. “It’s just unworkable, and basically it’s very difficult to squeeze large numbers of children into classrooms built in 1964 when the average class size back then was 18 students.”

Mollie Regan said her son is one of 31 students in a fifth-grade class at Wolftrap Elementary, also in Vienna.

“The problem is, even at a great school, when you are in a class with 31 kids — even with a great teacher — it doesn’t matter,” Regan said. “Thirty-one kids is too many.”

Garza said that fiscal problems have caught up with the 184,500-student school system and that her new administration must address a shortfall driven by “uncontrollable” costs, including $24 million in rising employee health-care expenses.

With the school system’s enrollment expected to reach 188,000 next year, Garza said, the influx of students will require about $25 million in related costs, partly because of the growing number of students needing English language instruction and of those who qualify for free or reduced-price meals, a federal measure of poverty. Since 2010, the number of students requiring English as a second language instruction has increased 51 percent, and the number of students eligible for meal subsidies has grown 25 percent.

“The challenges we face today in regard to these cost drivers will only continue in coming years,” Garza said.

Although Garza calls for eliminating 731 school system positions, she also proposes creating 368 new positions to handle the system’s rising enrollment. Some of the teachers whose jobs would be cut could reapply for the new jobs, she said.

Ted Velkoff (At Large), a School Board member and chairman of its budget committee, said he hoped this year’s budget process will ameliorate the administration’s historically frayed relationship with the county.

“I think trying to deal with this on an annual basis is difficult, and it’s stressful,” Velkoff said.