I'm reasonably certain that's not a fern.

Could you show us a close-up of the flowers?

Looks like one of the Aparagus 'ferns'. ie Asparagus species and not true ferns. I'm not that familiar with them and this one is not fully leafed out but compare with Asparagus densiflorus.

It could be asparagus, but I don't think so...I lean toward aster or other composite (desert adapted types with needle leaves)

If it has or develops thorns on the stems, compare to A. sprengeri. That has bulbous moisture storage roots, impossible to pull up, must be dug.

Thank you for helping me to sort this out! I don't have any flowers to show you, but here is a closeup of a frond or stem.

And one more view of the same frond.

No sign of thorns yet. It is still changing a lot day to day. I may have to wait until it gets a little further along before it starts matching up to pictures of your suggestions. Thanks again all!

Wait, I take that back: thorns are developing; they are downward pointing from the junctions of the branches. They are still soft so I hadn't noticed them yet.

What I thought might be flowers seem to be dark tips of new growth.

If you look at the bottom left you can see some new shoots which are unmistakably Aparagus spears right down to the scales at the base. The ends of the shoots are also very characteristic. There's no doubt in my mind that it is an Asparagus species.

No doubt in my mind, either.

Thanks again everyone. I'll watch for the white flowers and red berries that will make my "uninteresting fern" a bit more interesting.... and I won't let the dog eat the poisonous berries. :)