The USPTO posts on its website (www.uspto.gov) that it will remain open during the government shutdown:

“During the general government shutdown that began October 1, 2013, the United States Patent and Trademark Office will remain open, using prior year reserve fee collections to operate as usual for approximately four weeks. We continue to assess our fee collections compared to our operating requirements to determine how long we will be able to operate in this capacity during a general government shutdown. We will provide an update as more definitive information becomes available.

Should we exhaust these reserve funds before the general government shutdown comes to an end, USPTO would shut down at that time, although a very small staff would continue to work to accept new applications and maintain IT infrastructure, among other functions.”