Check out sphinx moth. They hover like a hummingbird or dragonfly would and have a similar wing span. Guessing...
hortster

Dragonfly, hummingbird moth WAG from sparse info provided. Can WAG sphinx moth too.

Dan

I looked at the images for sphinx moth, but that's not it. The wings on the insect I saw were thin, like a dragonfly's wings, not big like a moth. I guess if I see it again, I'll try to watch if it lands. This one just circled around me and then flew away.

Could be a Damselfly.

OOPS! Forgot the link.

Here is a link that might be useful: Damselflies of NM

We're getting closer to what I saw, but mine had even a thicker body than the damselflies on the website. As I think back on it, I'm not even sure I saw the wings; just a thick, long body.It had to have wings since it was flying, I just can't remember them. I believe I use to see this bug back in New York as a child, during the summer. It used to scare us, looking as menacing as it does, but we were assured it was harmless. I thought I remember people saying it was a dragonfly, but I'm not sure.

Was it, perhaps, New Mexico's state insect?

{{gwi:288455}}

Yikes!

I was thinking in terms of a dobsonfly.

What is NM state bug? That wasn't what I saw but that is an impressive bug. Mine did not have a 2 piece body but had a chunky piece behind it's head. Again, I didn't see any wings, so they were probably kind of transparent, if that makes any sense.

After looking at New Mexico insects on Google images, I saw one that looked close. It's called a western flying adder. The images of that bug had more colors than the one I saw which seemed all black. Again, I only saw it for a few moments, so it could have had colors I didn't notice.

The guy in the picture I posted (not my picture by the way)is a tarantula hawk. We have them her in So Cal too. You can't see it in the picture but when the sun hits them just right, they are a deep luminescent blue. Absolutely gorgeous, if you're into that sort of thing (which I certainly am).

So....in other words: a dragon fly.