On October 3, California Governor Jerry Brown signed a law, known as Assembly Bill 60, which requires the California Department of Motor Vehicles to issue driver's licenses to undocumented persons who can (i) provide identity, (ii) prove California residency, and (iii) pass the driving exams. The law will go into effect no later than January 1, 2015.
See http://legiscan.com/CA/text/AB60/2013 for the full text of Assembly Bill 60.
Other states with similar access to driver's licenses in place or soon to be effective include Washington, Oregon, Nevada, Utah, Colorado, New Mexico, Illinois, Maryland, Vermont and Connecticut. (See map of current driver's license laws at: http://www.nilc.org/driverlicensemap.html)