The US Congress is expected to be late in passing a budget. As a consequence, certain federal government operations may shut down after October 1, 2013.
Majority of the USCIS functions will carry on, since they are primarily funded through user fees. However, expect DOL functions to be interrupted because they are funded through appropriations.
If the government shuts for budgetary reasons, all but "essential" government employees are furloughed and not allowed to work.
USCIS: will be operating, except for E-Verify, if the government does shut down.
DOS: if there is a shutdown, the only visa processing will be for "life or death" emergencies. In prior budget-related shutdowns, DOS has continued to provide diplomatic visas and has been
wont to say "a really, really important business meeting is not life or death."
CBP: Inspection and law enforcement are considered "essential personnel," though staffing may be more limited than usual. The borders will be open, and CBP is unsure of how the shutdown will affect the processing of applications filed at the border.
DOL: it would likely cease processing all applications in the event of a government shutdown. If there is a shutdown, DOL personnel will not be available to respond to e-mail or other inquiries.