One of the most "robust" signals from global climate models run under scenarios of increasing human greenhouse gas emissions is an even drier climate in the Southwestern U.S. than exists there currently.
The 2009 report "Global Climate Change Impacts in the United States" from the U.S. Global Change Research Program (a report which the EPA relied upon in making its "Endangerment Finding" from carbon dioxide and other greenhouse gases) has this to say about the prospects of future drought in the U.S. (p. 33):
"In the future, droughts are likely to become more frequent and severe in some regions. The Southwest, in particular, is expected to experience increasing drought as changes in atmospheric circulation patterns cause the dry zone just outside the tropics to expand farther northward in the United States."
The 2007 Fourth Assessment Report of the IPCC (another report which the EPA relied heavily upon in making its "Endangerment Finding") had this to say (p. 890):