The name "camel spider" is misleading. They are actually solifuges, and they are not spiders at all. They are arachnids, but more closely related to scorpions and ticks.
While solifuges are found in many warm, arid regions around the world, they are not native to the United States. The creatures commonly mistaken for "camel spiders" in New Mexico are likely harvestmen (also called "daddy long legs"), which are harmless arachnids.
So, rest assured, if you're in New Mexico, you don't need to worry about encountering a "camel spider."