The Los Angeles County Board of Supervisors opened deliberations on its $24.53 billion budget Monday but put off a decision until Tuesday to determine if the county can fund a 65-cent-an-hour raise for in-home support services employees.

Although most wages throughout the county are expected to be frozen for the next fiscal year, some supervisors are mulling a raise for employees who care for disabled and elderly residents in their homes. The workers now make $9 an hour.

The cost to the county would be $21.5 million, but the funding would come from the state, said Lori Glasgow, deputy to Supervisor Michael D. Antonovich.