Three days before they are scheduled to vote on Mayor Antonio Villaraigosa's proposed budget, council members jockeyed Friday to find ways to avoid hundreds of layoffs, by proposing fees, reworking the numbers and demanding concessions from public employees.

Council President Eric Garcetti offered a plan to preserve as many as 1,000 jobs by counting, at least tentatively, on revenue from the mayor's plan to lease 10 public parking garages.

Councilman Herb Wesson went even further, proposing no layoffs at all.

The council's Budget and Finance Committee recommended the elimination of 1,761 positions last week. Wesson said he would push an array of new budget proposals, including fees on ambulance service and dog licenses and demand $63 million in concessions from the workforce.

"We're optimistic that if labor sees that this is the mountain they have to climb, they will, in fact, deliver," Wesson said.

While Wesson and Garcetti talked up their budget proposals, Villaraigosa held a separate news conference where he urged the council to spare his own antigang program from $1.3 million in cuts.

The mayor's budget, which takes effect July 1, calls for fewer library hours, the closure of an animal shelter and the elimination of 24 child-care centers. Branch libraries would lose one day per week. Regional libraries would fall from 60 to 40 hours a week starting July 1, according to budget officials.

The mayor described his antigang program, which sends intervention workers into high-crime neighborhoods, as an essential public safety initiative. "Keeping those programs whole, particularly in these times, is absolutely critical," he said.

While Villaraigosa advocated on behalf of his gang-prevention efforts, Garcetti pushed his colleagues to count on $53 million that the mayor expects from his plan to lease parking garages to private companies.

The council's budget committee said last week that the city should not depend on that money, since the bidding process has not been completed. Garcetti persuaded six of his fellow council members to support a plan that would place the parking money in the city's "unappropriated balance" - a fund for money that may or may not materialize.

If the parking money fails to come in by Oct. 1, the council would need to move ahead with plans for eliminating the 1,000 jobs, aides to Garcetti said. Villaraigosa and the council have eliminated 2,500 positions so far, mostly through early retirement or by transferring workers to city agencies that are unaffected by the budget crisis.

Even if the parking money arrives on time, the council would still need to vote Monday on an estimated 761 job cuts and up to 26 furlough days for each worker over a 12-month period. Garcetti said those reductions could be avoided if the city's labor unions come up with $57 million in permanent concessions.

Bob Schoonover, president of Service Employees International Union Local 721, voiced doubts about more givebacks from his members. "We already did that," he said.