Lots of good answers I see...
Get Out Of Dodge and go directly to Fort Apache. The border zone is a war zone. Staying there would be foolish. Airline, cruise ship and overland passengers are being checked for proper immigration documents (FMT until FMM arrives 1 May). I know for a fact that the army and FPP (Policia Preventiva Federal) are checking bus passengers south of the "Border Tourist Zone" for illegals. A person may (or may not) bluff their way past an inspection without an FMT but the officer is going to demand to see a valid passport. Driver license just doesn't cut it anymore. No FMT or Passport and oops, the person is detained until examined by an INM officer. Several days later they are bussed back to the waiting arms of the CPB.
After 1 May the old tourist card goes away forever. The FMM allows a stay in Mexico of one hundred eighty days in a three hundred sixty five day period. No more going to the border, turning around and getting another tourist card. The system is computerized just like the car permits. All FMM's must be turned in at the border or a police report showing the FMM was reported stolen. If an FMM holder does not turn in the form when leaving, that's the last time they can enter Mexico and obtain an FMM. Bienvenidos A Hermano Mayor.
Counting yesterday in the last week alone on the highway I was checked three times, for FM-3 and car papers. All were minutely examined. There were two buses over on the side as well with all passengers disembarked. I did not notice if any looked like other than Mexican origin.
The Days of Butch Cassidy & the Sundance Kid like tripping across the border are gone forever. But, areas like Ensenada, and San Felipe are less strict. Re-entering the USA without proper ID usually involves the entrant supplying their fingerprints, which are electronically submitted to the NCIC (National Criminal Information Center) for database analysis. The Customs own computer searches for wants and warrants. This all takes a lot of time, and does not even touch on the subject of sometimes intense grilling. Those folks can be rude and aggressive.
Good Luck