Faced with a budget gap of between $25 million and $50 million next fiscal year, the Arlington County Board has instructed the county manager to cut spending by $11 million and publicly warned that a tax increase is likely.

The gap is the first indication of what Arlington faces in the coming year, as its staff forecasts slow or flat growth in real estate taxes, which provide 60 percent of the county’s revenue, as well as the uncertainties connected to federal budget negotiations. County Manager Barbara Donnellan, who will spend the next several months working on her proposed budget, has already ordered a hiring slowdown, early retirement offers to some employees and departmental expenditure reductions.

The board’s guidance ordered Donnellan to maintain the portion of the budget devoted to Arlington schools at 45.8 percent, and funding to manage increased enrollment should be handled with a tax increase. School costs are expected to rise by $24 million.

Apart from the schools, the cost of compensation and health care for the county’s 3,200 full-time positions is going up, and Arlington is also facing increased costs associated with affordable housing , safety-net programs and land acquisition.

Taxpayers may be asked to fund increased costs associated with a project to connect county and schools facilities to a fiber-optic network. The Arlington Mill community center is expected to cost an additional $2.7 million, and the franchise agreement with Comcast is also expected to become more expensive, officials said.

The board also told the manager to provide it with two assessments: What would be cut if tax rates were kept the same and how much tax rates would go up if services were kept equal to the current fiscal year.

The board’s guidance is just the start of the staff’s work on the fiscal 2014 budget, which is typically finalized in late spring before the July 1 start of the budget year. The entire budget is expected to come in at $1.06 billion.

But that first step started out with disagreement Saturday, as vice chair Walter Tejada and Chris Zimmerman dissented in a 3 to 2 vote.

The pair unsuccessfully pushed for a major increase in spending on affordable housing and small-business retention, particularly in the Columbia Pike area, from about $9 million each year to $25 million annually within the next four years.

Tejada and Zimmerman argued that maintaining the status quo will push the county further behind as costs continue to rise.

Their surprise amendment irritated board member Jay Fisette, who noted that the same proposal had been voted down twice before the past year.

“Are you kidding me?” Fisette said. “I’m just a little frustrated by having this debate constantly. In fact, the advocates here are going to hurt themselves if they keep doing this.”

Fisette called the proposal “irresponsible” because it would tie the hands of the county when the economic forecast is unsettled. He also said would increase the tax rate by five cents, in addition to the three cents currently devoted to housing.

Board members Libby Garvey and chair Mary Hynes agreed. Garvey reminded others that a staff affordable housing study is underway, and she noted that 5 percent of the budget is already devoted to the issue.

“I think we could spend 10 percent, 15 percent, 20 percent [of the budget on affordable housing] and probably not meet the need,” Garvey said.

Hynes said that no one should question the board’s commitment to affordable housing, but the board has to balance other “very ambitious goals important to the life and vitality of this community.” She said she does not rule out an increase to the affordable housing fund but that it should come during the next few months’ budget discussions.

A community forum on the budget is planned for 7 p.m. Nov. 29 in the Washington-Lee High School cafeteria.