I found a wealth of background information on Prop 73, which would require parental notification for a minor to have an abortion, at the USC California Policy Institute, and wading through it all has me convinced that Prop 73 is not a good idea. Of course in an ideal world, we would like to see teens with an undesired pregnancy be comfortable in discussing the issue of abortion with their parents, and come to a decision that all are happy about. And it turns out that most teens in that situation do turn to at least one parent to come to their decision. For the smaller portion who don't, in some cases they have legitimate fear of abuse or other adverse repercussions. The evidence indicates that teens are generally capable of making abortion decisions that they do not regret later on, and that a higher proportion of those who made a decision independently were satisfied with their decision than those who were pushed by their parents into a decision other than what they would have liked. There is also some evidence that parental notification laws, rather than having the intended effect of increasing family communication, instead have the effect of pushing teens into other options such as seeking an abortion in another state, obtaining a "back room" abortion, or attempting it themselves. The bottom line is that most teens will discuss the matter with a parent, and for those who feel unable to, a law is not going to magically improve their family relationships.
As if that weren't enough, the text of the proposition contains wording describing abortion as "the death of the unborn child", which may have unintended consequences beyond this proposition if it becomes installed in the State Constitution. (Actually, some would argue that the consequences are fully intended by the proposition's proponents, intending to establish a pro-life beach-head in the Constitution.) A parental notification statute in Pennsylvania containing a nearly identical phrase has had the unintended(?) consequence of constraining stem cell research in that state. California, having just authorized a substantial state investment in stem cell research, certainly doesn't need this to become a spanner in the works.
The proponents' argument in the ballot pamphlet starts with the observation that a teenager can't get a flu shot or even an aspirin from the school nurse without parents being notified, but they can have an abortion in secret. Granted that's a jarring juxtaposition, but what's wrong with that picture is that the school nurse can't give a child an aspirin without fear of being sued. In the case of reproductive health services, the state has long recognized the importance of teens having confidential access to such services, and because of their importance, have created a special "safe haven" for teens who need such services and the medical practitioners who treat them. (Such laws go back to the 1950s, so I would say they have stood the test of time.)
Finally, one should keep in mind the larger picture, in that teen pregnancy rates, birth rates, and abortion rates have been dropping nationwide in the last 15 years, and even more so in California than the nation overall. Obviously the policies of the last 15 years are moving us in the right direction, and this misguided proposition seems unlikely to improve that and would possibly move us backwards.