The comment I replied to claims Cali has an $80B surplus. Seems like there's plenty there for a rainy day fund. Anyway, whether or not you can raise taxes is pretty immaterial to a rainy day fund--it's just a matter of whether or not it's prioritized. If California can't prioritize said fund now, then it wouldn't be able to do so with prop13 (it would just find other uses for the revenue).
