Fairfax school officials learned Tuesday that the county is unlikely to close a $45 million hole in the schools' budget, although the two boards vowed to continue working to resolve the shortfall by next month's deadline.

The county is working to close a $169 million budget gap of its own, County Executive Ed Long said, which makes it difficult to fund the school maintenance projects, bus replacements and program expansions that the School Board wants.

When coupled with uncertainties stemming from massive federal spending cuts that kicked in this month, that shortfall has left the county guessing on the best way to prepare next year's budget.

"It doesn't look like our challenges are going to end anytime soon," he said.

All of that is bad news for the county's school system, which accounts for more than half of the county's general fund spending. Without an increase in county funding, school officials would have to find the money they need elsewhere or begin making cuts of their own to combat increased costs.

Teacher raises, new programs and a spike in student enrollment have all widened the schools' budget gap. And Long's 2014 proposal to transfer $1.72 billion to the system from the county budget falls short of the $45 million the schools need to break even.

"We're just growing too much," said Fairfax County Public Schools Superintendent Jack Dale, noting that the student population has surged by 9 percent to 181,500 students since 2007.

School officials, meeting with the full Board of Supervisors for the first time since both entities unveiled their fiscal 2014 budgets, urged the county to help them close their funding gap and keep up with the demands of their students.

School board member Megan McLaughlin, of the Braddock District, told board members not to back down from Long's proposed 2-cent property tax hike to avoid a hit to everyday services, while county Supervisor Pat Herrity, R-Springfield, questioned why the schools have yet to hire an auditor to help identify wasteful spending.

Their arguments were met with opposition, however, and the two boards left Tuesday's meeting having agreed to nothing.

"I urge us to sit down together and talk together," said county Supervisor Cathy Hudgins, D-Hunter Mill. "We need to be developing a budget together."

The two boards will continue working on the budget until the county's April 30 deadline to adopt it.