One of the users at The Firearm Blog has called the ATF and it seems like they have stopped processing all NFA paperwork as a result of the shutdown.
I called [the BATFE] today and Vicky (a pleasant sounding lady who answered the phone) said they have been affected by the government shutdown. Staff furloughed, no applications are being processed, nor can they check status. My Form 4 was sent in Feb 2013, so who knows when I’ll see it.
I guess the ATF is not an essential government function.