With steep state budget cuts under debate in Sacramento, Los Angeles County supervisors voted Tuesday to push for changes to CalWorks and other government aid programs they said would save nearly $270 million.

Included in their suggestions is a novel proposal: Put unemployed parents to work caring for their own children.

“What we’re saying is do not cut Welfare to Work outright: Target the cuts to the people who are the most expensive,” said Miguel Santana, a deputy to the county’s chief executive.

Parents now receiving assistance must attend job training and search for work. While they fulfill those requirements, they are eligible for subsidized child care, which typically costs the state about $500 a month per child in L.A. County.

The parents of children under age 1 may stay home and still receive benefits. Now, county officials propose expanding that to parents who have one child under age 2 or two children under age 6. Monthly job training and child-care costs for such parents often exceed their welfare check, Santana said.

In Los Angeles County, 8,000 households with more than one child under age 6 receive CalWorks-subsidized child care, according to the county’s department of social services. If adopted, county officials estimate the proposal -- intended to counter Gov. Arnold Schwarzenegger’s threat to eliminate CalWorks -- could save the state $140 million this fiscal year.

Some parents who would be affected by the change had mixed feelings.

After Antoinette Levenson’s husband was laid off by a boat dealership two years ago, the mother of two applied for cash assistance and joined the state’s Welfare to Work program.

Now Levenson, 27, is about six months from earning her associate degree in culinary arts and has a job lined up at Ralphs. She receives about $750 a month in assistance. The state also pays about $1,000 a month for her sons, Jaden, 4, and Gavyn, 2, to attend Canyon Vista Children’s Learning Center in Chatsworth while she finishes school.

“If I had it my way, I’d stay home all day with my kids,” Levenson said as she dropped the boys off Tuesday. “Then again, I love day care. My kids have learned so much.”

Although Levenson said she is not sure she could replace her eldest son’s preschool teachers, she is willing to try.

“There’s times I just drive by and watch the kids,” she said. “You’ll never be able to get the kids’ little years back.”

But Priscilla Murillo of Canoga Park, a single mother with three children under age 5, said she wants to finish school and find a job as soon as possible. With her youngest child just a month old, Murillo, 27, could stay home now and still receive benefits. But she said the Welfare to Work program motivated her to continue pursuing her associate degree.

Murillo worries that if the state pays fellow single mothers to stay home, they will become dependent on welfare.

“I think it’s good to push people,” she said. “It helps them and it helps the economy.”

Child-care providers also said they are concerned about looming cuts.

Michael Olenick, who heads the nonprofit Child Care Resource Center in Chatsworth, said 12,000 child-care staff members and parents in northern L.A. County alone rely on CalWorks.

“For many of them, it’s the only source of revenue that they have,” Olenick said of the CalWorks subsidies. “If they lose the revenue, then they end up on cash aid as well.”

On Tuesday, a legislative budget committee in Sacramento rejected the governor’s plan to eliminate CalWorks, proposing instead to cut it by $270 million. Those cuts include $175 million in reductions to child-care and employment services.

That would allow the county to move forward with its proposal, said Philip K. Browning, director of the county Department of Public Social Services.

“But it’s still not a done deal -- the governor hasn’t signed off on it yet,” Browning said.

A spokeswoman for the governor said he will continue to push for the elimination of CalWorks but remains open to other options as he tries to close the $24.3-billion budget shortfall.

County supervisors -- who plan to pursue a waiver to get federal welfare funds even if CalWorks is eliminated -- also proposed Tuesday that the state cap and overhaul general relief for single people, as well as reduce payments to adoptive parents, disabled foster children and some child-care providers.

The proposal to allow more parents to stay home troubled some of the county supervisors, including Supervisor Mike Antonovich, who voted against exempting parents of children under age 2 from Welfare to Work.

“They should be seeking employment. In the long term it benefits everyone in the county,” Antonovich said.

Supervisor Gloria Molina grudgingly voted yes.

“It doesn’t fit with the spirit of Welfare to Work, but we’re in a different situation,” Molina said. “What we’re doing is trying to say to them don’t eliminate Welfare to Work -- here are some savings.”

molly.hennessy-fiske @latimes.com