Legal Question in Landlord & Tenant Law in California

If you do not move within the 60 days, the landlord can file an unlawful detainer (eviction) lawsuit against you and the court could order you to move.

You might check to find out if the property is covered by a rent stabilization act. If so, the landlord must provide legally-enumerated good cause reasons for eviction. If it is not covered, then you might try to negotiate with the landlord an earlier move-out date in exchange for a reasonable payment to cover your moving expenses and aggravation.