Possibly, but not likely. There are legal theories such as promissory estoppel which might entitle you to monetary damages. But realistically, unless the landlord either signs a written renewed lease or accepts a rent payment from you to cover the month after June 30, 2013, you don't have much to stand on. Upon expiration of the lease, the landlord can file an unlawful detainer lawsuit to evict you WITHOUT needing to serve you with any further notice.
Frank W. Chen has been licensed to practice law in California since 1988. The information presented here is general in nature and is not intended, nor should be construed, as legal advice for a particular case. This Avvo.com posting does not create any attorney-client relationship with the author. For specific advice about your particular situation, please consult with your own attorney.