This is for 2012 payroll.

Not sure what you mean by 'applicable.'
Work is work and all work affects your SSDI. It's supposed to be reported the minute it starts, not at the end of the year.

Sorry! SDI, not SSDI. I don't know about CA SDI, and there are different types anyway. I'd get on the ca.gov website and find your plan. I assume you are handling the payroll.

The Texas company is telling me that they do not need to withhold California SDI since the work is not performed in California but in Texas.

Not sure how someone lives in CA while working in TX - but assuming this is a short-term work assignment in TX: the worker does not pay CA SDI on the pay he earns while assigned to the job site in TX.

No, I am not handling the payroll but that was my field when I worked so I am somewhat familiar with what is appropriate. The employer did not make me feel confident with their answers when I questioned them.

The SDI wording is 'work as an employee in the state of California.'
This means that even if your employer is based in CA, you are not working in CA.
If your employer is based in TX, I don't know why this is even a matter of debate.
Then there's the matter of how the IRS defines state of residence.

The company is based in Texas and plans are to commute and work several weeks of the month in Texas but still maintain residence in California.

If this is intended to be a long term job (> 1 year) I would argue this makes you a TX resident. The good news then is that you should not owe CA any income tax on these wages! You can still maintain a CA home - just think of it as your vacation home. The savings to you can be dramatic. However, you must make it clear that you consider yourself a TX resident - for example I would suggest that you get a TX drivers license and start using your TX mailing address for tax purposes.

I did this myself - a number of years ago I moved to TX while my wife and kids stayed in NJ, and so I avoided NJ income tax on my TX wages. My wife was still working in NJ and so had to pay NJ tax on her wages, but at least I saved the taxes on my wages.

Thanks to everyone for your responses. It has been very helpful