If you are using the TurboTax online editions there are no e-file fees for filing either a federal or state tax return. The TurboTax account fees are for the use of the software to assist in completing a tax return. The account fees are the same whether the tax return is e-filed or printed.
If you cannot pay for the state program then the state tax return cannot be filed. You can use a friend or relative's credit card to pay the TurboTax fees.
You can efile the CA return online for free ... https://www.ftb.ca.gov/file/ways-to-file/online/index.html
There appears to be a filing fee of $25.00 for CA State return efile with electronic payment of taxes. But TT will not allow input of credit card to pay.
@Ibeardsley That is normally caused by a problem with your computer. You can try clearing the cache and cookies on your computer. You can google how to do that for your operating system if you don't know how. Also, you can try logging into TurboTax using a different web browser.