I think visa processing is not affected ....From CNN:
Is it safe to fly?
Airport security personnel are considered essential, so travelers please continue to follow Transportation Security Administration rules about liquids, shoes and other restrictions at the airport.
Air traffic controllers, some safety inspectors and other essential employees will "continue working in order to maintain the safety of the national airspace system," said the Federal Aviation Administration, in an e-mailed statement. "Safety is our top priority."
Most immigration, border and customs employees are also considered essential personnel, which means passport controls at U.S. borders and points of entry like airports and cruise ports -- should be unaffected by the shutdown.
Other FAA projects, including facility security inspections, routine personnel security background investigations and development of the next generation of air traffic control technology, will be placed on hold.
What if you're waiting on a passport?
If you're waiting on a U.S. passport, how long that wait will last depends on where the passport agency is located. Passport services, because they are funded by other revenue, are generally "unaffected by a government shutdown," according to a State Department spokesperson.
There's just one possible catch: If the passport office is located within a government building that has been shut down, passport approvals may be affected.
If you need a visa
Because consular services at U.S. embassies and consulates around the world are largely funded by application fees, not annual appropriations, visa applications filed by foreigners wanting to enter the United States will continue to be processed, according to the State Department.