There are more than one of those. There is a private 2nd and there are several set up through CalFHA. The City Programs are almost all the CalFHA
They have their good points and bad points.
The private one has a higher rate but it will usually close on time. They CALHFA has a lower rate but never closes on a timely fashion, it also requires a higher credit score. I have only done one of these and it closed three months after it was supposed to. I had sellers and sellers agents calling me every day screaming. That was in 2000 I have never done another one. They have such a bad reputation for closing late that many agents advise sellers not to accept offers containing this type of loan. So be ready to make a lot of offers. Your agent will earn every cent of that commission.
So what to do. The problem is that once they CALFHA loans are a week or so late, the sellers cancel the sale and go with someone else. Trust me the stress and hard feelings are not worth it.
But we have the problem of the other one being so expensive. Not such a problem really because in 6 months we can streamline refinance to a less expensive FHA loan ( assuming that rates stay the same. This might not be a good assumptions.)
If you are going to try the CalFHA or Chdap I would recommend going with Sheryl Arndt below, she seems to do a lot of them and so that may be your best bet.