Thank you to everyone who has answered so far.
Let me provide some additional information, which should answer the questions posed in your replies. We are taking a cruise which ends in San Diego. Therefore the flight must leave after 11 a.m. Plus, we have to be back at work the next day so the flight must reach SJU before 5:30 a.m. Which, from what I've been able to find, leaves only the following options:
1- American Airlines SAN - LAX - MIA - SJU (This is the flight I'm asking about here.)
2- American Airlines SAN - DFW - SJU (My brother doesn't like this one because it arrives at 5:22 a.m. so if anything is delayed there will be a problem)
3- Jetblue SAN - JFK - SJU (JFK in January sounds risky in terms of weather.)
4- Southwest SAN - AUS - MCO and Jetblue MCO - SJU (Requires airline change and, therefore, baggage pickup and rechecking plus going through security again. The time between flights is only 2 hours, which is not enough to make me very comfortable with that. We were originally planning to do this one because Southwest used to have a direct flight between SAN and MCO which left a very comfortable 5+ hr connection in MCO.)
As an additional question, how common are delays at LAX? The connection time in MIA is 1 hr 33 min and I've been to that airport a couple of times. However, the connection time obviously cannot handle a significant delay.