According to AILA, most USCIS operations will not be affected by a government shutdown, since USCIS is funded by user fees rather than by congressional appropriations:
http://aila.org/content/default.aspx?docid=35062
Presumably this means that oath ceremonies administered by the USCIS would go ahead as scheduled. However, I am not sure what would happen to judicial oaths that are administered by the federal courts rather than by USCIS.