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.