I'm not familiar with caterpillars of the Southwest, but they look like some type of budworm. There are many different types in the east, including some that decorate themselves with the flower's petals!

They all make a moth. Hopefully, someone else will know which type it is.

Sherry

Thanks, Sherry. I looked it up and I'm thinking it is a grey pug moth. The markings are similar, and when I poke at it gently, it gets rigid like a twig. I was Googling it and one site mentioned that it does do that.

if you go to" Butterflys and Moths of North America" they can identify your caterpillars for you.It is a realy neat site.