This sounds like one of the unicorn plants (Ram's Horns or Devil's Claws), Genus Proboscidea. There are four species that occur in New Mexico, three of which occur in our Native Plant Database. Without flowers or leaves you probably won't be able to determine which of the species your seed cases are from, but you can see exactly where each has been found in New Mexico by clicking on New Mexico on the distribution map for each of the species on its USDA Plants Database page:
Here is an interesting article about the Devil's Claws from Wayne's World.