With every seat filled in the Los Angeles City Council chambers Wednesday, Anita Edwards had one minute to make her case before the buzzer cut her off.

“I’m here because I’m fighting for my job,” said the 51-year-old city child-care director, one of hundreds of employees expecting a pink slip by July. “I love what I do and that’s why I’ve stayed dedicated to this city for 18 years.”

For as long as anyone can remember, city leaders have neatly balanced their books by eliminating vacant positions and shifting money between accounts. But now the first of as many as 4,000 job cuts are underway to keep the city solvent. And that has thrust into public view what is usually a very private process. Confrontations between vulnerable workers and their elected representatives have begun to roll out on a live telecast of the council’s meetings each week and on the city’s website, lacity.org.

A week ago, council members listened uncomfortably from their leather swivel chairs as half a dozen technicians from the city’s public access channel begged for a last-minute reprieve. On Wednesday, in an effort organized by labor unions, council members faced a stream of city employees such as Edwards, who urged them not to go through with layoffs that would virtually shut down the city’s licensed child-care programs and curtail hours at libraries and recreation centers.

The lineup included young patrons such as Zachary Novakovich, who said that if council members closed his child-care center in Glassell Park his mother could no longer hold her job. “If she doesn’t go to work then we can’t stay in our house,” he said.

Moments later, Arthur Jackson, who works at a recreation center in South Los Angeles, warned against cutting jobs like his. “We work in some of the toughest parts of the city, and I do it without a gun or a badge,” he told the council. “If you think we have a gang problem now, watch what happens if we close these parks.”

Councilman Tom LaBonge said city employees facing layoffs have buttonholed him in the hallway. Last week he got a sheaf of drawings from elementary school children urging him not to fire their favorite librarian, Hillary George of the Will & Ariel Durant Branch Library in Hollywood.

“Ms. Hillary” appeared Wednesday before the council in a swishing lime skirt and bubble gum-sized pearls urging members to find a more “creative” solution. Of the 20 librarians on the layoff list so far, George said, she would be No. 12 in seniority.

“This has been a long drama, but it’s just gotten a lot more dramatic,” LaBonge said. “You can’t save every job.”

Those pressures have led to messy scenes that could play out again and again in the months ahead.

The task of drawing up the layoff list belongs to the department heads, who answer to the mayor, leaving some council members feeling powerless about which jobs are cut.

Last week, after hearing from the technicians at the city’s public-access channel, Councilman Bill Rosendahl shouted at the general manager of the Information Technology Agency, demanding to know why she had chosen those jobs.

This week, City Clerk June Lagmay, who is grappling with diminished staff due to layoffs and early retirements, appeared on the verge of tears as she explained that she simply did not have enough employees to handle all of the department’s responsibilities.

And reinforcing the notion that no layoff notice is final, several council members have seemed to pluck money out of the air to save certain positions. After Councilwoman Janice Hahn publicly questioned the dismissal of a curator at the Point Fermin Lighthouse in San Pedro Bay, the job was quietly restored.

Hahn and Councilman Herb Wesson have promised to dip into their discretionary accounts to temporarily rehire three arts instructors.

With those kinds of maneuvers, Councilman Tony Cardenas worries about picking “winners and losers” and creating false hope for hundreds of employees down the line -- many of whom will get pink slips on July 1 when a labor deal no longer protects them.

“They’re going to look to us and say ‘save my job,’ ” he said. “At that time we’re going to be in a worse position to try to save even two or three jobs.”

maeve.reston@latimes.com