Fairfax County faces a budget gap of $114.4 million in the coming fiscal year that could hamper efforts to boost school funding, County Executive Anthony Griffin said Tuesday.

In a preview of the county’s budget, Griffin said that he hoped to include a 5 percent increase in school funding — which accounts for nearly 53 percent of the county’s general fund spending — to meet rising school enrollments and other needs. That would mean nearly $81 million extra for a school district whose student body is expected to top 181,000 students next year.

But Griffin also warned members of the Board of Supervisors and the School Board “not to bank” on the increase because of the cloudy economic outlook.

As the county continues to shake off the effects of the worst recession in generations, Griffin suggested that the Board of Supervisors will once again be looking at a spending plan that allows little room for new initiatives. Residents could face a slightly higher effective property tax and higher fees to pay for county services, he said.

“It’ll be ‘Groundhog Day’ in terms of the budget,” Griffin said, referring to the movie in which events play out the same way every year.

One of the biggest uncertainties at the moment, Griffin said, is whether Virginia will shift more responsibility to the county for maintenance of its roads, as some members of Gov. Robert F. McDonnell’s administration appear to be considering.

County officials have been unhappy for years about the state’s inability to keep up with potholes, unmown medians and other routine wear and tear, and some members of the Board of Supervisors have advocated assuming more control. But county officials also worry that the commonwealth will give the county more responsibility without the funding to carry it out.

Griffin, emphasizing he was making a back-of-the-envelope estimate, said taking over road maintenance could cost $100 million a year, or about 5 cents of the county’s current property tax rate of $1.07 per $100 of assessed value. If the state handed over responsibility for roads without the money to handle it, he said, the result could be “quite painful.”

With the economy still drifting and state and federal finances also in flux, Griffin suggested that the county will probably remain on a tight spending leash for at least five more years.

Now that the election is past and all members of the Board of Supervisors have been returned to office, their attention is shifting toward putting together a spending plan for fiscal 2013, which begins July 1. It is also the last budget that Griffin is likely to shape as county executive, having announced plans to retire next spring.

On Tuesday, Griffin gave a rundown of the county’s financial outlook during a joint budget committee meeting with the School Board and the Board of Supervisors. Several newly elected school board members also attended.

Under the scenario Griffin outlined, the county would spend $80.5 million more on schools. The county would also spend nearly $50 million more to cover a 3 percent raise for its employees next year, as well as the 2 percent raise already granted this year. He noted that the pay increase follows three consecutive years in which all or a portion of county employees’ pay was frozen.

Griffin said he also anticipates spending an additional $16.6 million on debt service, $11.8 million more on pensions and health insurance benefits and an additional $5 million on fuel. The overall increase in spending for fiscal 2013 was projected at nearly $179 million.

At the same time, he said that revenues — which rely heavily on property taxes — bottomed out in fiscal 2011 and appear headed 2.8 percent higher in fiscal 2013. Direct aid from the state and federal governments is also expected to decline, though he noted that such funds make up only a small percentage of overall revenues.

To make up the shortfall, Griffin said he planned to tap reserves and ask agencies to trim 1 to 5 percent in spending. But Griffin’s draft budget would also ask residents to pay more in fees and property taxes.

The typical homeowner, whose property was assessed at $449,275, would pay about $4,807, or $40 more than last year. He noted that the effective tax bill on that property has dropped by about the same amount since fiscal 2007.

Griffin, in offering a preview of the assumptions that he is including in a draft budget, also gave the Board of Supervisors’ budget committee a snapshot of the county’s fiscal health. He said the county is still one of only eight states, 39 counties and 33 cities to retain a Triple A rating at the nation’s three major credit-rating agencies. He said general fund spending has increased only $24.9 million, or 0.7 percent, since fiscal 2007, while the county has eliminated 499 positions in the past three years.