As a result several government agencies, providing immigration-related services, are impacted:
USCIS
Status: All USCIS offices worldwide are open and individuals should report to interviews and appointments as scheduled. Since most of USCIS’ budget is derived from fees paid by applicants and petitioners filing nonimmigrant and immigrant visa petitions, it is the least impacted government agency.
• E-Verify is currently unavailable due to the government shutdown.
DOL
Status: All DOL services are shutdown. DOL (OFLC) will neither accept nor process any applications or related materials (such as audit responses), it receives, including Labor Condition Applications, Applications for Prevailing Wage Determination, Applications for Temporary Employment Certification, or Applications for Permanent Employment Certification. OFLC’s web site, including the iCERT Visa Portal System, is static and unable to process any requests or allow authorized users to access their online accounts.
DOS
Status: Normal operations for the time being. U.S. embassies and consulates around the world will continue as many normal operations as possible; operating status and available funding will need to be monitored continuously and closely. Check the U.S. embassy/consulate website for more information.
More information on government offices affected by the shutdown is available via the +AILA National website below.
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AILA – What Happens During a Government Shutdown (Updated 10/1/13)
In general, if the government shuts for budgetary reasons, all but “essential” government are furloughed and not allowed to work, including immigration agencies. Update from 10/1/13 includes information from DHS, USCIS on E-Verify and updated information from DOS and EOIR.