Fairfax County executive Edward L. Long Jr. proposed a budget Tuesday that would address a projected shortfall by cutting 45 county jobs, offering limited raises for government employees and allocating $14 million less than what the county school system asked for.

The $3.81 billion general-fund budget does not call for an increase in residential property taxes, which Long purposely avoided in a year when residents are already primed to see an average property tax hike of $185 because of increases in home assessments.

It cuts about $25 million from libraries, family programs and other services — difficult trims, Long said, after several years of reductions triggered by the 2008 recession.

“We tried to maintain core services,” Long said of the budget, which also delays some planned investments in county computer networks and other projects. “All the choices are bad.”

Before adopting a final budget in late April, the Board of Supervisors will hold public hearings on the draft budget and vote on whether to keep the county’s residential tax rate at $1.09 per $100 of assessed value.

The lingering effects of federal sequestration cuts and a sputtering local economy have led to declines in commercial tax revenue in Fairfax and a 15.2 percent office vacancy rate — the worst since 1991.

As a result, last fall, Long projected a $100 million budget shortfall, which was later revised to about $89 million. To address it, he proposed a menu of spending increases and sacrifices, prompting complaints on Tuesday from supervisors and others.

For schools, Long offered $2.01 billion in county funding — a $66.7 million increase. That proposal falls short of the $2.4 billion spending plan the School Board adopted this month.

School officials say they need the full amount to pay for full-day Mondays, $70 million in raises for teachers and other costs in the fast-growing system.

“We had hoped the county executive would have recognized that the school board’s advertised budget is a realistic and pragmatic plan that deserves full funding,” Superintendent Karen Garza said in a statement. “We’re hopeful the supervisors will support additional funding to prevent further reductions in classroom programs.”

Long recommended a total of $9.46 million in raises for the county’s 12,000 workers — an increase of about 0.84 percent, or half of the 1.68 percent rate at which the cost of living has increased over the past year. He also eliminated a net of 45 jobs.

To address concerns about Fairfax losing its AAA bond rating, Long proposed adding $8.57 million to county pension plans, moving them closer to being funded at 90 percent. Wall Street rating agencies have threatened to downgrade Fairfax debt if the pensions are not funded at or near that threshold, and that could lead to higher long-term debt payments.

Long also recommended increasing emergency budget reserves above the current 5 percent of general-fund spending, which rating agencies also have cited as a concern. “We’re at the lower rate of our reserves for a triple-A jurisdiction,” he warned supervisors. “We simply cannot do that.”

Several supervisors expressed frustration over the options.

Supervisor John C. Cook (R-Braddock) questioned shifting more money to pension funds without long-term reforms in those programs.

Supervisor Jeff C. McKay (D-Lee) said he’s worried that a proposal to leave vacant four urban-planning positions will hurt revitalization efforts.

And Supervisor Penelope A. Gross (D-Mason) said the proposal to curtail raises could spoil the “sweet spot” reached in relations between county officials and employee unions.

“This makes it a little sour,” Gross said.

In all, said Supervisor Catherine M. Hudgins (D-Hunter Mill), the entire draft budget “is a bit sobering.”

T. Rees Shapiro contributed to this report.