County Administrator Susan Muranishi said the funding gap is the largest that the county has ever had.
In a statement, Muranishi said, "It is a responsible budget that will allow this county to live within its means and remain solvent, while maintaining many important services that our residents depend on."
But, referring to the possibility of further cutbacks in state funding due to the state's fiscal problems, Muranishi said, "We must be mindful, however, that further cuts are on the horizon."
Muranishi said in a briefing with reporters two weeks ago that about half of the 235 positions that are being eliminated are currently filled.
According to a spokesman for the county, the Board of Supervisors left the door open to averting some of the planned layoffs by asking employee bargaining units to consider concessions in ongoing labor negotiations.
The $2.4 billion is an increase of $34.7 million, or 1.45 percent, over the final budget for the current fiscal year, which ends on June 30.
Supervisor Keith Carson, who chairs the county's budget work group, said in a statement, "I am not in favor of the proposed reductions, but we are backed into a corner as a result of the current economic crisis."
Carson said the reductions "will have a devastating impact on people's lives" and warned that further reductions in state funding "undoubtedly will push many over the cliff."
The approval by the Board of Supervisors at a short meeting today followed two days of public hearings earlier this week at which the board heard emotional testimony about the impacts of proposed cuts to public safety, health care and social services programs.
Alameda County Sheriff Greg Ahern said at a hearing on Tuesday that budget cuts would force him to close the Fairmont Animal Shelter in San Leandro.
But the Board of Supervisors today directed county staff to investigate possible cost-saving options that might avoid having to close the shelter.