Absolutely nothing wrong with a healthy concern about diving below 60ft. Especially in MoCal diving. Diving deeper requires a lot of attention. As TSandM states, you're more alert on gas consumption and NDL/MDL times. In addition, conditions can be quite dramatic at depth. However, as others states, the more experience you have, the more comfortable you will be. With more diving, you'll know how much gas you typically use and you'll get an understanding of how much time you have at depth.
I also agree with everyone that there is a skills component as well. Practicing air shares and slow ascents will build confidence in your and your buddy's ability to deal with an emergency if it arises. Also, doing basic buoyancy so you feel absolutely sure you can hold you position without finning or sculling will go a long way to your comfort level.
I still remember my first boat dive in Monterey. Prior, I had dove in Austin, Roatan and Maui. What I quickly found was that doing a free water ascent in significant swell was more more hair raising in cold water than doing the free water ascent in calmer warm water spots. While I really count the easy shore diving as a blessing for MoCal, it can also be a crutch. Since it's following a shore on ascents, you don't do a lot of open water ascents. This just needs to be practiced.
Best of luck, and the deeper stuff will be there when you're ready.