Macro...those leaves were about an inch long..

First impression, probably totally off the mark, is Araujia sericifera (Moth vine).

Leaves a bit on the small side, though, but that could easily be environmental.

Are you certain it is a vine and not just a lax shrub?

(Moth vine does not appear to have felted leaves.)

What about this one? Atriplex torreyi var. griffithsii, Griffiths Saltbush, Southwest Desert Flora

Definately Chenopodiaceae. Atriplex has a lot of leaf variation, so maybe Atriplex torreyi var. griffithsii or maybe Atriplex argentea?

Hmm, it says that Atriplex torreyi var. griffithsii (Griffiths Saltbush) is very rare in the United States at it is only found in only Willcox, Arizona...so I'm guessing it's not that one? But, it doesn't really seem to resemble Atriplex argentea (Silver Saltweed), either?

You could have revisited the site and gotten an updated pic showing new growth, which might give us more to go on, but we've exhausted every lead, and there's nothing more that can be speculated from these old pics. The only other option I can glean from these 2 photos is that it's Convolvulus arevensis thats been sprayed with herbicide that messed up it's leaf texture? These could be juvinile leaves on a species that has different looking mature foliage? Not many plants have saggitate/hastate leaves that look like that.

Sorry...this was at a plant rescue during a limited, allotted window at a construction site out-of-town. So, whatever this plant was, is probably sadly bulldozed gone now...

I would rule out herbicide though, because it was a pretty pristine plot of land that was practically all natives.

But thanks and sincerely appreciate all your hard efforts!!!