If you are US or CAN, you need to go to your consulate to get a replacement. The US consulate is in Nuevo on the 2nd floor of the Paradise Village Mall. An emergency replacement is about $150. They aren’t open on the weekends, only until 1pm during the week.
To fly within Mexico, you only need a photo ID.
It’s good practice to keep a copy of all of your ID on your phone and with someone back home. This can help to speed up the process of a replacement. You will still need to replace your passport from the US once you return, the temporary passport issued here is only good for 1 year.