I have always wondered why these plants are in the Asteraceae and under the microscope, it is immediately obvious. There are both ray and disk flowers in a tiny inflorescence. Working with these tiny flowers under the microscope is going to be the trick.
Note that at one time both A. millefolium and A. lanulosa were recognized. The thought was that A. lanulosa was native and A. millefolium was introduced and that the two could be distinguished. This idea has been abandoned, and I think rightly so.
Begin with the key on page 830 in "Arizona Flora"
Bilabiate corollas? No. All strap shaped corollas? No. Rays present? Yes. Pappus with bristles? No. Pappus none? Yes. this takes us to GI scan the key for G on page 837 to ensure I am on the right track. Achillea is there.
Rays white? Yes. Receptacle naked? No. Rays sessile and persistent on the achenes? No. Leaves alternate? Yes. Heads very small? Yes. Achillea (108)The key describes the heads as dense flattish or rounded cymose panicles. Two questions here are tricky. One is about the receptacle being naked. The trick here is that a scale comes loose with each tiny flower I pluck off, these scales count to make the receptacle paleaceous (it has thin translucent scales, or would once these dry out and the seeds fall off). The other tricky question is about the rays being persistent. There is really no way I can tell with fresh material, so this involves a guess or checking both paths in the key. The other options would be Zinnia or Sanvitalia.
The description on page 936 describes the plant as thinly or densely pilose, sometimes silky canescent. It has creeping rootstocks (who would have known?). My specimen certainly has lots of long hairs, mostly parallel and now laying against the stem or leaves.
Tom's Plant pages / tom@mmto.org