CA state landlord tenant law, tenant's right to break lease upon landlord's request for tenant to obtain co-signer

The answer depends on whether you have taken possession of the property or not. If you have taken possession (i.e. moved into the property) you may not be able to break the lease without the Landlords consent. If you have not moved in, your signature on the lease is considered only a proposal to rent the premises and it is up to the Landlord to accept. Since the Lanlord requires additional assurance in the form of a co-signer you may not be in lease agreement at all and as such may not have to do anything to get out of the lease, because the Lanlord has indicated that the did not accept your proposal for lack of a co-signer.