Correction: Earlier versions of this article included proposed funding that is not part of the operating budget in the 2015 budget figure.

The head of the Fairfax County Board of Supervisors said Tuesday that she may try to increase the property tax rate to generate more funds for schools and other services after County Executive Edward L. Long Jr. unveiled a budget proposal that fell far short of what school officials have sought.

Chairman Sharon Bulova (D) said she will consult with colleagues to consider advertising a higher tax-rate cap. If the county were to meet the public school system’s full budget request, the rate could have to go as high as $1.115 per $100 of assessed value, she said. That would add about $150 to the average homeowner’s tax bill — on top of an estimated $332 jump expected this year because of higher residential real estate assessments. The current rate is $1.085 per $100 of assessed value.

On Tuesday, Long proposed a $3.7 billion general fund budget for fiscal 2015, including a boost in school spending of $34.3 million. Long was adhering to a promise by the Board of Supervisors to cap any increase in school funding at roughly 2 percent.

About 51 percent of the county’s budget goes toward funding the 184,000-student school system, a proportion regularly cited by supervisors during what has become an annual tug-of-war over school funding.

Under state law, county officials have until next week to set a new tax-rate ceiling.

The possibility of an increase pleased school Superintendent Karen Garza, who pronounced Long’s budget proposal “very disappointing.”

“While they say the schools are the priority, in my mind it was not reflected in Ed Long’s budget,” Garza said. “I think we have to remain optimistic and hopeful that our county leadership sees how desperate the schools are for additional revenue.”

Ilryong Moon, the School Board’s chairman, called Long’s budget proposal “absurd.”

The property-tax rate has crept up slightly in recent years in Fairfax, a relatively affluent jurisdiction of 1.1 million people. It was increased by 1 cent last year and by half a cent the year before after being trimmed by 2 cents for fiscal 2012. Every penny increase in the rate means an average of $50 more in a homeowner’s tax bill.

The School Board recently approved a $2.5 billion budget based on receiving $63 million more from the county than Long included in his proposal. The budget approved by the board would cut 730 staff positions and increase classroom size while granting $41 million in raises for teachers.

The county is hoping that state officials in Richmond can make up some of the difference between the proposal and what school officials say is needed to stave off more-drastic cuts. Fairfax is awaiting approval to receive about $27 million in restored state education funds geared toward competitive teacher salaries, officials said.

Long’s draft budget projects a $10.6 million surplus during fiscal 2015. A $39.4 million deficit had previously been projected.

Long said the county has weathered the negative impacts of federal sequestration cuts. A stronger housing market has led to about $126 million more in property tax revenue through higher assessments, his office said.

Although the county’s unemployment rate — 3.6 percent — is well below the national average, the commercial real estate market is still suffering with an office vacancy rate of nearly 15 percent, the highest since 1991. Long urged caution before allowing developers in neighborhoods such as Tysons Corner and Reston to build more office towers without having tenants in place.

The draft budget proposes increasing spending on infrastructure and economic-development efforts, investments that Long argued are essential for Fairfax’s long-term financial health. It also grants 2 percent raises to the county’s 14,000 non-school employees, an amount county unions immediately called insufficient.

“Everybody forgets about the general employees in Fairfax,” said Randy Creller, chairman of the county’s Employee Advisory Council. He said the average county employee salary of $63,000 a year is “still behind the curve.”

Several public hearings and question-and-answer sessions are scheduled before a final budget is adopted in April.

Supervisors expressed mixed feelings over the possibility of raising property taxes, with some saying an increase would disproportionately affect low-income residents and others saying one is needed to keep schools and other county services intact.

“I’d like to say something good about this budget,” said Supervisor John C. Cook (R-Braddock). “And when I find something, I’ll let you know.”