This clean, friendly Mexican place makes a nice break from the long drive on I-10 across southern NM. I stopped for lunch last week: good shredded-beef tacos, nice, creamy refritos, very good chips & salsa. Popular place, with good reason. It's in west Deming on the main drag, diagonally across from the Sonic drivein and 1 blk W of McDonalds.
Note that the Deming Truck Terminal at the west Deming exit usually has the best gas price along this stretch. And, if you've never gone to the Deming-Luna-Mimbres museum, you should.