Faced with a $35 million budget gap and an uncertain economic future, Arlington County Manager Barbara Donnellan on Wednesday recommended a tax increase that will cost the average single-family homeowner an additional $262 in property taxes next year.

Forty-six of the county government’s 3,749 jobs would be eliminated, although only 20 of the jobs due to be cut are now staffed. Employees would lose a paid holiday — Columbus Day — but not the hopes for a pay raise: $3.6 million is still budgeted for raises that come with merit step increases.

Donnellan, who briefed the County Board in advance of its regular Saturday meeting, said she was “very anxious about putting a 3.2 cent [property tax rate] increase in the base budget,” given the county’s high commercial vacancy rates, the threat of major federal budget cuts and stalled property tax values throughout the county. But she said the budget would maintain the services that county residents say they want. The tax rate would rise to $1.003 per $100 of assessed value. The county budget would be $1.07 billion, an increase of about 2 percent.

County Board members, who now start two months of work on the fiscal 2014 budget before they decide what the tax rate will be, asked several questions about how the county is planning for the federal budget cuts known as sequestration.

“A lot of families in Arlington have one or more people who work for the federal government or federal contractors,” she said. “People are going to be taking pay cuts by being furloughed . . . that extra $262 is not going to be easy for them to find.”

Owners of a house worth $525,000, which the county staff say was the average assessment of a single-family home in Arlington, would pay about $5,263 in property taxes under Donnellan’s recommendation. But that homeowner probably saw the assessed value of the property go up 1 percent, unlike condo and commercial property owners, so the actual tax increase could be higher.

Most other taxes, such as personal property taxes, the annual decal fee, the garbage, water and sewer service, and the utility tax would not rise. Some fees, such as those for police at special events and park and recreation reservations, would go up modestly while fees for home improvement projects would go down.

About 1.2 cents of the proposed 3.2 cent tax increase would go to the schools, which expect almost 1,000 more students to enroll next fall. The schools would receive $411.1 million, up $10.8 million, from the county under this budget.

Four-tenths of a cent of the tax increase would go to pay for new non-school facilities such the Arlington Mill community center on Columbia Pike and Connect Arlington, a telecommunications fiber network to connect all schools and county buildings. The other half of the tax increase would be devoted to general county government needs.

Donnellan noted that she and her staff also recommended $9.3 million in budget reductions and adjustments.

In addition to the 46 job cuts, 20 more staffers took early retirement and the hiring of replacements has been slowed. Among the jobs lost will be seven in the police department, three in the fire department and 15 in the human services department, she said. The public safety jobs will be reduced through attrition, she said.

Donnellan sought the public’s advice on what cuts they preferred through several online budget chats during the past few months.

“I haven’t found a program yet that didn’t have a constituency,” she said Wednesday.

The County Board will hold several public work sessions starting next week, with public hearings March 26 and 28. It has scheduled a vote for April 20.