Well, the good news is that the call-in system frees you up for the most part for the entire week you are required to serve. You call in the night before to see if you have to appear the next day. That happens every night for the entire week. You may never even have to set foot in the courthouse.
Of course, if you have missed a prior jury duty assignment, they may actually require you to come in on day one. However, I happen to know that if you do that, then LA County does the one day/one jury and done. After one day of sitting in the jury selection room, unless you are selected that day, you're done. And also consider that quite a lot of their juries last only a matter of hours, or maybe a day or two at the most.
If you are selected for a jury, and that jury is going to take the whole week or longer, then yes, you will get an opportunity to bring this up with the judge in that case and potentially get excused. On top of all of this, there's no guarantee that you would actually get through voirdire and be seated on the jury.