I live in CA too, but my disability insurance is through a private insurance company my former employer uses, so I am not very familiar with CA state disability/fed social security either. I have a very basic (and hopefully not inaccurate…lol) understanding of how this all works. Basically, you can have CA Short Term Disability for up to 52 weeks, and then need to apply for Social Security Disability Income or Supplemental Security Income (federal programs) for further coverage. http://www.ssa.gov/disability/
I believe that applying for SSDI is often quite a lengthy process, and people are frequently turned down the first time they apply. You are only eligible for SSDI if you have worked for a certain number of years (paid into it long enough), otherwise you can apply for SSI, which is a needs-based program and has income restrictions. I am not totally clear on the finer details of how this all goes together, but it is my understanding that yes, anything beyond 52 weeks and you are dealing with the federal government (social security), not the state. I do know that there are non-profits out there that will help you with these kinds of questions, as well as assistance with your application(s).
Best of luck to you.