Hello Gardengus and anyone who was wondering about this plant. I asked a Professor and sent photos to a Professor at NMSU. He believes the plant is purslane. But, the tiny white flowers are believed to be Dodder. A parasitic plant that threads in and produces tiny white flowers from formed seedpods from the parasitic plant. Wow! I sure have learned a lot! Thankyou Gardengus for you
r help with this question!