Read here. Droughts are a frequent visitor to the southwest U.S. and Mexico regions. The current drought that this area is experiencing is bad but in no way is it as extreme as the droughts that took place during the Medieval era.
As the chart reveals, both the Medieval and modern periods share a characteristic of high incoming solar irradiance. With the increase of incoming solar energy, the result is time spans of frequent and more intense droughts. These more extreme droughts occur naturally and have nothing to do with greenhouse gases, including CO2 emissions.
There are some scientists who predict we are entering a stage where 60-year droughts, like those during the Medieval Period, could occur but no one knows for sure. If solar irradiance falls (as it seems to be doing most recently), the modern drought cycle may end.
Woodhouse et al. published this 1,200 year perspective of Southwestern North America droughts:
"The medieval period was characterized by widespread and regionally severe, sustained drought in western North America. Proxy data documenting drought indicate centuries-long periods of increased aridity across the central and western U.S...The recent drought, thus far, pales hydrologically in comparison... Spatially, the mid-12th century drought covers all of the western U.S. and northern Mexico...whereas the 21st century drought has not impacted parts of the Pacific Northwest...The 21st century drought has lasted about a decade so far, whereas the 12th century medieval drought persisted with an extent and severity...for two decades, 1140–1159 [AD]...In both instrumental and paleoclimatic records, periods of sustained drought in the Southwest have often been concurrent with elevated temperatures. The warmest such episode, in the mid-12th century, was more extensive and much more persistent than any modern drought experienced to date..." [Connie A. Woodhouse, David M. Meko, Glen M. MacDonald, Dave W. Stahle, Edward R. Cooke 2009: Proceedings of the National Academy of Sciences]