You need one to get a DL. It's a bit misleading on their website because they say a Canadian passport is acceptable as proof, but then later on it says you must show you are able to stay for at least another 60 days in order to get a licence, and the only way to do that is with an I-94 if you're in a non-immigrant classification. Basically if you're there as a visitor in B-1 or B-2 it's pointless because the licence would only be valid for a few months.
They seem to be iffy about the SSN:
http://dmv.ca.gov/dl/dl_info.htm#SSN
One of my relatives tried to get one without an SSN, basically they require the SSN if you can get one. If you were there, say as TD or H-4 and couldn't get an SSN, then you can get a DL but you need proof you can't get one. My relative said it seems to depend on the office, because she tried another office and they didn't seem to care, but by then she had it anyway.
Steve.