Field Bindweed

This looks very much like Field Bindweed. If it eventually gets morning glory type flowers in white or pink, we’ll know for sure.
Bindweed is considered a noxious wed in many parts of the country (including Colorado). The roots can run underground 12″ a day, and any piece of the root can create a new plant. The seeds can lie dormant for decades and then germinate for a new round. It can run under mulch, and the parts that stick up at the edge can generate enough energy to feed all the covered leaves and stems.
Great patience and persistence are required to control this weed by hand. Here are a couple of links that you might find helpful:
http://www.ext.colostate.edu/ptlk/1552.html
http://www.ipm.ucdavis.edu/PMG/PESTNOTES/pn7462.html