The SSA has put a plan together detailing what operations will continue and what tasks will not be undertaken in the event of a government shutdown. The SSA has released its Shutdown 2013 Potocol (link opens a 5-page PDF).
Take a look. Charts on page 3 show what activities the Field Offices and DDS offices will continue, and what activities they will discontinue, during the a shutdown.
The chart on page 4 shows the activities the ODARs will continue, and what activities the ODARs will discontinue. Continued ODAR activities are limited to hearing cases and deciding cases. Judging by the long list of discontinued activities, including decision-writing, it seems clear that hearing offices are going to be pretty hard hit in the event of a shut down. Scheduled hearings will continue. But that is about it.
Let's hope it does not last very long. If it does, it's not going to be pretty for those of us practicing in this area.
Update: I stopped by the Portland hearing office yesterday. Hearings are continuing, but the office is in disarray.