It hasn’t been clear how fully staffed the Board’s headquarters in Falls Church were going to be if the government shut down today.  An e-mail this morning from EOIR provides a bit more detail:

The Board of Immigration Appeals (BIA) is processing emergency stay requests as well as cases where the alien is detained, including case appeals, motions, federal court remands, and bonds. The stay line is open (for emergency stay calls only), but all other telephone lines have been switched to closed status. The BIA Clerk’s Office staff is accepting all filings and will be open Monday through Friday, from 8:00 a.m. until 4:30 p.m.

So, it looks like the emergency stay line will remain open, but calls to the clerk’s office won’t be answered.  I just called the USCIS Customer Service line, and they’re open for business (spoke with a real human being).