" Only difficulty is that my home state has no state tax, so unfortunately just because of few days, I would be paying too much tax in CA."---> Then you can claim the CA state taxes paid to CA on your federal return by claiming your itemized deduction on Sch A line 5( only itemize if the deductions are greater than your standard deduction for your filing status); however, you can't (don't) claim your itemized deductions , thenyou can't deduct your CA state taxes that you paid to CA on your return. I guess you may need to adjust your W4 form to adjust the numer of withholding alowances with your employer to properly determine taxes withheld from your paychecks.
Please visit the IRS website here( you can follow the instructions on W-4);
http://www.irs.gov/pub/irs-pdf/fw4.pdf?portlet=3
" I was hoping that by claiming that signing was done outside the CA then it shouldn't be counted as CA earning. But looks like that can't be done."--->No i don't think so; it was CA that you earned the income, so you must report it to CA not outside CA.