Correction: An earlier version of this story misidentified Kimberly Adams. She is president of the Fairfax Education Association. The story has been corrected.

The Fairfax County Board of Supervisors on Tuesday kicked off a series of public hearings on a proposed budget for the 2015 fiscal year that, on the first day, boiled down to two points:

Few residents are happy about the options for spending on schools, police and other services next year. And the arguments for and against higher taxes are equally passionate in the wealthy county that nonetheless is hampered by an anemic economy in some areas.

“How can you justify such a huge tax increase?” asked Charles McAndrew, referring to a higher cap on the county’s real estate tax rate that he said could mean about $600 more per year on his Oak Hill home if the rate were fully realized.

Judith Harbeck countered, pushing for more county funds targeting the festering problems in her Mount Vernon neighborhood. “Please: Raise my taxes. We need to increase the pie, not just cut smaller slices,” she said.

The two hearings Tuesday were marked by rallies by groups pushing one cause or another — a ritual for Fairfax officials trying to meet increasing demands in the increasingly urban county.

On Tuesday, Republicans United for Tax Relief demonstrated inside the government center as county employees headed to the parking lot at the end of their workday.

Some of those same county workers planned to rally Wednesday in support of higher wages and more spending on schools, followed by advocates for more spending on libraries.

County police officers who are seeking higher wages for officers who have less experience plan to rally after a hearing on Thursday.

“We’re asking the supervisors to treat their budget like the average family treats its budget by not placing an extra burden on others as they seek to spend within their means,” said James Parmelee, chairman of the Northern Virginia Republican Political Action Committee, which organized an anti-tax rally Tuesday.

But with the county’s school district predicting dire cuts without an extra $63.8 million in funding, and the still-weak economy bringing in less revenue for spending in other areas, making the numbers work in the proposed $3.7 billion budget has been a complicated exercise.

School employees and other advocates asked the supervisors to increase taxes in order to provide additional funding to classrooms.

“It is demoralizing to stand before you year after year to ask you to do the right thing for Fairfax school employees,” said Precious Crabtree, an elementary school art teacher. “It is such a tired game. Your inability to understand the school system’s needs [is] obvious.”

Steven Greenberg, president of the Fairfax County Federation of Teachers, whipped out a black cape, a Darth Vader mask and played a recording of “The Imperial March” from the “Star Wars” franchise.

“All this debate about the budget brings out the dark side in all of us,” Greenberg said before promoting an increase in the county transfer to benefit schools.

In hopes of creating some flexibility in spending, the board recently voted to advertise a higher property tax rate cap to $1.105 per $100 of assessed value — an increase from $1.085 per $100 of assessed value that could provide county officials with an extra $43.8 million if the new rate were to go that high.

The higher cap would increase an average homeowner’s annual tax bill by $100, on top of the extra $332, on average, that homeowners will see from projected higher property assessments.

County officials are also considering a series of spending cuts next year, including $4 million in construction projects related to compliance with the Americans with Disabilities Act and a $1 million ambulance replacement fund.

Kathy Kaplan argued that repeated cuts to county libraries are hurting Fairfax’s long-term prospects for economic vitality by leaving small-business owners without accessible information that could help their companies grow.

Moreover, she said, library cuts contribute to illiteracy in the county.

“This isn’t just about the children’s story-time program,” she said. “If they don’t turn it around right away, the libraries will be crippled for a very long time.”

During an evening hearing on the budget, Fairfax school officials sought to emphasize the urgency behind allocating more funds to keep up with the steady growth in the school system of 184,000 students.

“We have reached a tipping point where the underfunding of our schools at both the county and state levels . . . suggests that there is very real and troubling evidence that our great school system is beginning to show signs of decline,” said Ilryong Moon, chairman of the school board.

Kimberly Adams, president of local Fairfax Education Association, agreed that the county is at a critical juncture. She warned that county employees are becoming increasingly restless with the pay they’re getting in Fairfax. Her union is planning an “Invest in Fairfax” rally on Wednesday.

What’s at stake, Adams said, is the county’s quality of life for years to come if quality government workers become frustrated and decide to leave.

“We’re going to lose people who know the system, who know this area, who know what Fairfax County is and what we expect,” she said. “I want the best fireman, the best policeman and the best fourth-grade teacher that we can possibly have, but we’re not funding that.”