It appears that you must have a valid passport to enter Mexico, see e.g. the following links:
Mexican Consulate in San Francisco,
Effective March 1st 2010, all US Citizens are required to present U. S. Passport or U.S. Passport Card when entering Mexico (traveling by air, land or sea).
US Permanent Residents traveling by air, land or sea to Mexico are required to present a valid Permanent Resident Card. Plus a valid and not expired passport or travel document. If you do not have that card consult other documentation also accepted to prove the US Permanent Residence status.
Mexican Consulate in Detroit, http://consulmex.sre.gob.mx/detroit/index.php/info-english
US Permanent Residents traveling by air, land or sea to Mexico are required to present a valid Permanent Residency Card, as well as a valid passport from their country of origin or travel document.
Mexican Consulate in Anchorage
All permanent residents of the United States who are holders of a “Permanent Resident Card”, also known as “green card”, who want to travel to Mexico as tourists just need to present their passport and “Green Card”.
More importantly, Timatic (the database that airlines use) says that
- Passports and/or passport replacing documents must be valid
- Warning: if departing from the USA (regardless of any destination passport exemptions), a valid passport and/oraccepted departure document For details, click here is required by the US immigration authorities.
- Holders of emergency or temporary passports.
Airline employees will use this Timatic information when they decide whether to let you board your flight to Mexico. Most likely, they will not let you board the plane (even if an immigration officer in Mexico may let you in).
I would suggest that you contact a Mexican consulate and your airline, and double check with them whether you need a valid passport.