Real Estate Law
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Unfortunately, there's no way to stop the landlord from proceeding with the eviction if the rent has lapsed and the lease is in default. Thus, you are doing the right thing by trying to find alternate housing. But, you should have some time to vacate....usually, you'd have at least until the court hearing, and more than likely the judge will give you some time after the hearing (10 days or so) to vacate the premises.
Here's a good link you can read: http://www.dca.ca.gov/publications/landlordbook/evictions.shtml
Here's another good link: http://traklawoffice.com/2010/09/key-provisions-of-calfornia-residential-landlord-tenant-law/
Per the link, a hearing is required to occur within 21 days, so you've probably got at least that much time to get your affairs in order IF the landlord will not work something out with you.