The Fairfax County Board of Supervisors, voting along party lines Tuesday, agreed to consider raising the property tax rate by one cent for the next fiscal year’s budget.

Sharon Bulova, chair of the Fairfax County Board of Supervisors. (Michael S. Williamson/WASHINGTON POST)

The board’s vote Tuesday sets only an upper limit as part of its budget deliberations. Supervisors could adopt a budget without changing the current property tax rate of $1.07, as used by County Executive Anthony H. Griffin in his proposed budget. At that rate, the typical homeowner would pay $34 more in property taxes because of rising home values. But Griffin also said the board might want to consider a property tax rate of as much as $1.09 if members wished to approach the amount requested by Fairfax County Public Schools.

“I’m meeting us in the middle,” said Board Chairwoman Sharon S. Bulova (D), who proposed considering a higher rate. She said the county needed more flexibility in considering its budget, especially because legislative initiatives or budget cuts by the Virginia General Assembly’s budget could force the county to take up the slack. Her motion carried 6-3, with one supervisor absent.

Fairfax County executive Anthony Griffin. (James M. Thresher/THE WASHINGTON POST)

“No matter what we call the stormwater fee, whether it’s a tax or a fee, it is based on the value of your home,” Frey said. “We can’t forget the homeowner pays it.”

But Supervisor Catherine M. Hudgins (D-Hunter Mill), who said she supported the higher tax rate although she was not able to attend Tuesday’s meeting in time to vote, said many constituents have been calling for the board to restore previous cuts, such as reductions in library hours.

“It is the door to the community. It is critical,” Hudgins said of the public library. “For many children, for many immigrant families, it is the only connection they have outside their neighborhood.”

Supervisor Gerald W. Hyland (D-Mount Vernon) also suggested that the board’s decision to set an higher limit on the tax rate does not mean the supervisors will adopt a budget at that level.

“We’re going to have to push hard to go above that with some members,” he said.

Griffin’s draft $6.7 billion budget, which he unveiled last week, would boost spending by about 2 percent.

The fiscal 2013 budget projects general fund revenue of $3.46 billion, an increase of about $112.4 million, or 3.4 percent, and an increase in spending of $59.25 million, or 1.71 percent, from the revised fiscal 2012 spending plan. Total general fund expenditures are projected at $3.521 billion.

Under Griffin’s budget, the storm water rate would from 1.5 to 2.5 cents per $100 of assessed real estate value.

Griffin’s budget also anticipates increasing the amount for county schools for operations and debt service by about 4.5 percent, to $1.85 billion. The School Board has requested $2.45 billion, an amount that is nearly $136 million, or 8.4 percent, more compared with the current fiscal year.