As far as I know, there are no programs in California that allow you to use the tax credit as a down payment.
As for your problems finding a home, I completely understand. It is a very frustrating time for home buyers in the market today. Here are a couple of thoughts that may help you. First, when anyone, bank or homeowner, sells a home, they get cash. Your loan funds and the seller gets the cash. The big benefit of a cash offer to a bank is that it is much more likely to close escrow than an offer that includes a loan. In many cases, a bank will accept a lower cash offer even if they have higher loan offers, simply because they will close.
Second, if this is the case, you need to make your offer as strong as possible. Have your lender do a complete application, not just a pre-qualification. If possible, get all the underwriters requirements up front. Be able to demonstrate to the bank that you can in fact close escrow. Check into local county down-payment assistance programs. These programs are starting to get funding again, and could free up your cash on hand for other costs.
Third, if you are using an FHA loan with 3.5% down and asking for closing costs, your offer is like one fish in a school of very similar fish. Figure out a way to come up with some or all of your closing costs. Ask relatives to help if they can. Don't ask for any repairs. The idea here is to make your offer stand out from all the others, and in most cases there will be plenty of other offers.
Finally, keep this in mind. The process right now is long and frustrating for most buyers. You can buy a home; but you are most likely going to lose a few first. The only way you won't get a home is if you quit now. Best of luck to you!