Had something similar on a UA flight to SJO last year. We were severely delayed due to weather out of IAH then had to fly quite far east around a storm before heading south. In the end, SJO was cloud covered and they would have had to circle, so there was an extremely quick turn and landing in LIR for fuel and to wait out the clouds/storm over SJO.

Actually a lot of people did want to get off in LIR as that was actually where many of us were going anyway. Because of the long delays in Houston, already they had to start letting some people off, so the captain pleaded with passengers not to demand getting off in LIR since if we did they would then have to cancel the flight. They said it's due to it turning into a domestic flight in Costa Rica if they let anyone off in LIR, so the remainder of the flight would have to be cancelled. In the end everyone stayed on to San Jose.

In your case, I can imagine since it's all domestic then they would have to let people off if demanded, depending on the length of the delay, however I'm unsure what would happen to checked luggage if there was any.