Hi Dave,
Hudsonian Godwit is something of a rarity in California (less than 20 records), and winters in S America. Marbled Godwit is a common winterer, especially in San Francisco Bay. I guess the closest good shorebird site to Palm Springs is the Salton Sea, which often gets wintering goodies such as Stilt Sandpiper. I don't know Southern California very well, perhaps you could try asking Andy at the LA Birding blog.
Good luck!
Richard