Karen Garza is vigorously defending her $2.5 billion budget request, which calls for staffing cuts but also for a 5.7 percent increase in taxpayer funding. Some school board members called it unrealistic. (Donnie Biggs/Fairfax County Public Schools)

Fairfax County Schools Superintendent Karen Garza vigorously defended her proposed $2.5 billion budget Monday as “reasonable” while some School Board members questioned her tactic of asking for far more than county supervisors have said they are willing to give.

Last week, immediately after Garza revealed her request — which calls for a 5.7 percent increase in taxpayer funding, or about $98 million more than last year — some county supervisors said the school system is being unrealistic. County supervisors have vowed to limit any increase to 2 percent.

Garza’s budget proposes $96 million in cuts that would eliminate 730 staff positions and increase class sizes at all grade levels. But it also calls for teacher pay raises and other increases.

During a work session Monday, School Board members said they don’t think they will receive the full amount of Garza’s funding request and worried that the proposed budget is far too optimistic, possibly setting up additional difficult cuts.

“I don’t think we’re going to get anywhere near 5.7 percent,” said Elizabeth Schultz (Springfield). “I think it’s on a wing and a prayer that we’re looking for 5.7.”

Megan McLaughlin (Braddock) agreed. “I am looking at this budget and seeing stuff we could do without,” she said. “Do I publicly say we don’t need 5.7 percent?”

Garza, who joined the school system before this school year and is presenting her first budget, responded by saying that her proposal is “very real” and still leaves the schools short.

“The key question is, do we think 5.7 is too much? Because, quite honestly, I don’t think it’s enough,” Garza said. “If we don’t get a 5.7 percent increase, it would be a travesty. It would be a travesty.”

Garza noted that as the school system continues to expand beyond its 184,600 students, budget demands also will grow.

“We can never lose sight of the fact that next year, we’re going to have these same problems time after time after time,” Garza said. “I think our community should expect a 5.7 percent increase and a long-term solution for our schools.”

County supervisors have described Garza’s plan as similar to business as usual. For years, supervisors have said, School Board members have been unwilling to live within their means and have made unreasonable budget requests. Members of the School Board have countered that while the school system has grown by 20,000 students since 2006, the county’s funding has not kept up with the surging enrollment.

School Board member Kathy L. Smith (Sully) said that the 5.7 percent increase is needed.

“We might not get it, and we might have tough decisions to make, but I agree that this is not enough,” Smith said. “So I am going to fight for this. . . . I am going to fight as hard as I can.”

Ted Velkoff (At Large), the School Board’s budget chairman, said this year’s budget development has been different than in years past. Velkoff said that Garza met extensively with parents, principals and supervisors while working to come up with a precise funding request.

“That has not been business as usual,” Velkoff said.

Garza’s predecessor, Jack D. Dale, revealed a $2.5 billion budget a year ago that included a 5.5 percent increase in county funding — worth about $92 million. Dale said last January that he knew his request was not realistic. “The reality is we probably won’t [get everything we ask for], because we never have,” he said.

In the end, supervisors approved a 2 percent increase in school funding.