No, no age limits for Seguro Popular, which is the main government program. Many expats in popular retirement havens like Lake Chapala and San Miguel de Allende enroll in SP for emergency only use and then pay out of pocket for routine care. Many also hedge their bets once they hit age 65 by enrolling in bare bones basic Medicare too in case they have to return to the U.S., while those few who have really cut ties discontinue paying into the U.S. system.
Hopefully there will be more options in the U.S. in future but worth knowing about Mexico and other south-of-the-border options - especially for things like assisted living/nursing home care. I know several couples who've moved to Mexico because one spouse needed such care and paying $1200 a month for great care is a whole lot more appealing than going broke paying $6000-8000 a month in the U.S.