Fairfax County, one of the region’s economic powerhouses, expects another year of tight budgets despite improvement in the economy, county officials say.

As the Board of Supervisors prepares to address a busy agenda Tuesday in its last regular meeting of the year, its members have been assessing County Executive Anthony H. Griffin’s cautious preview of next year’s budget.

Griffin said last week that a $114.4 million budget gap in the coming fiscal year could hamper efforts to boost school funding. Griffin said he hoped to include a 5 percent increase for school funding — which accounts for about 53 percent of general fund expenses — to meet rising enrollments and other needs. That would mean nearly $81 million extra for a school district that expects more than 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 worst recession in years, Griffin suggested that the Board of Supervisors will once again be looking at a spending plan with little room for new initiatives. Residents will probably 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 last week, referring to the movie in which events play out the same way every day. With the economy still drifting and state and federal finances in flux, Griffin suggested the county’s finances will probably be on a tight leash for at least five more years.

Members of the Board of Supervisors said they were not surprised.

“I don’t think we’ll see any new initiatives,” Supervisor Penelope A. Gross (D-Mason) said Friday. “We know that it’s a very small, incremental resurgence. Resurgence is probably too strong a word.”

The cautious outlook comes as the county, whose powers to raise revenue are limited by state law, is rounding up support in the hospitality industry to lobby the Virginia General Assembly to let Fairfax increase its lodging tax by 2 percent to build a conference center. Without strong backing from hoteliers and the Fairfax County Chamber of Commerce, the measure will probably die in the Republican-dominated legislature, county officials said.

Another uncertainty is whether Virginia will shift more responsibility to the county for maintenance of its secondary roads, as the administration of Gov. Robert F. McDonnell (R) appears to be considering.

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

Griffin — emphasizing that he was making a back­of-the-envelope estimate — said that taking charge of secondary road maintenance could cost Fairfax $100 million a year, or about 5 cents of the $1.07 property tax rate. If the state hands off responsibility without the money to pay for it, the result could be “quite painful,” he said.

In an op-ed published Friday in The Washington Post, Fairfax County Board of Supervisors Chairman Sharon Bulova (D) teamed with Republican counterparts from Loudoun and Prince William counties to argue that shifting such a responsibility from the state to local governments — a phenomenon known as devolution — would be a bad deal for Northern Virginia taxpayers.

Now that the election is past and all members of the Board of Supervisors have been returned to office, their attention has shifted 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.

Last week, Griffin sketched 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, Fairfax 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 granted this year. Griffin noted that the raises follow 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. He projected a total increase in spending of nearly $179 million.

At the same time, he said revenue — which relies heavily on property taxes — bottomed out in fiscal 2011 and appears headed 2.8 percent higher in fiscal 2013. Direct aid from the state and federal governments is expected to decline, although he said such funds make up only a small percentage of all revenue.

To close the budget gap, Griffin said he planned to tap reserves and trim 1 to 5 percent from agency spending. But his draft budget would also ask residents to pay more in fees and property taxes. A homeowner whose property was assessed at the county average of $449,275 would pay about $4,807, or $40 more than last year. He said the effective tax bill on that property has dropped by about the same amount since fiscal 2007.

Some elected officials said they were taken aback by Griffin’s assumption of a 5 percent increase in school funding, saying it could create unrealistic expectations among School Board members and the public.

“I thought it was a little bolder than I would have anticipated with constrained budgets,” Gross said, noting that last year’s transfer to schools had been flat.

Supervisor Michael R. Frey (R-Sully) also considered the figure too optimistic, especially because the county will feel the impact of federal and state spending cuts. Frey also expressed concern about possibly taking on road maintenance.

“The one thing I keep saying when we talk about it, is ‘Remember the car tax,’ ” Frey said, referring to former governor James S. Gilmore III (R)’s repeal of an annual tax on vehicles. Virginia later struggled to make up for the loss of revenue to local jurisdictions and eventually froze the state’s level of reimbursement to them.