I am currently a Florida resident and considering a job in California. I plan to reside in Florida and work in California. Am I responsible for any California income taxes?

Second, if I get a short term residence in California, does my tax situation change?

It does not matter if you have short term residence or not. If you are present in CA and have income during that period, you must file CA tax return and report that income.

You are responsible for paying CA income tax on any wages earned in CA. If you reside in FL then you would pay CA income tax only on your CA income. If you become a CA resident then the only real change is that any other income you may have (interest, dividends, capital gains, etc) would also be subject to CA tax.

Your state of residence is determind by where you sleep at night, so if you will be spending more nights in CA than FL you will be considered a CA resident. This is true even if you keep your home in FL.