Hi katn86.

Sorry I just saw your post. It's hard to tell what plant this is from the photo. Possibilities include jojoba, which has sort of fleshy leaves and female plants produce a nutlike fruit. It could also be an olive tree that's been heavily pruned for a while. Olives also produce fruit but you may not see them if it is pruned often.

Can you post a close up of the leaves/stems? That would help.

Not an expert, but I second the jojoba. They grow all over the desert near Tucson. They have a distinct, desert smell to them too -- a sweet-herbaceous smell.

Here is a link that might be useful: Other jojoba pictures