The United States Courts, which includes the U.S. Bankruptcy Courts, announced on its website that "in the event of a government shutdown on October 1, 2013, the federal Judiciary will remain open for business for approximately 10 business days. On or around October 15, 2013, the Judiciary will reassess its situation and provide further guidance. All proceedings and deadlines remain in effect as scheduled, unless otherwise advised. Case Management/Electronic Case Files (CM/ECF) will remain in operation for the electronic filing of documents with courts."
So that is good, the U.S. Courts will continue running as usual for now, and new cases and documents can continue to be filed. Not so sure about after Oct. 15, but hopefully the politicians will do what they are supposed to do, and reach some kind of compromise to resolve this impasse by then.