Most likely the US could halt 1/2 of its food production and still have plenty of food. We have no shortage of arable land, we have a greater shortage of people actually wanting to be farmers/ranchers :(
Not in terms of calories.
The rest of the US could live just fine without out-of-season artichokes or whatever.
Water is rather more important. You can live a long time on a plain diet (especially if you have vitamins available). Without the water, things in California would get very, very ugly, very, very quickly. ]
Also: what are you planning to do if (or maybe "when" would be better) Mexico decides that it wants to take back its former territory (i.e., all of California)?
I think an independent California would have a good relationship with Mexico. Though I'm interested in why you think we wouldn't.