This is from a law firm's news letter:
As a fee-based agency, USCIS will continue to accept and process applications and petitions. However, we expect there to be delays in processing, as some support staff may be furloughed and USCIS depends on non-essential agencies for services.
E-Verify will be shut down. According to the Department of Homeland Security, “citizens and U.S. businesses will not be able to access E-Verify, the Internet based system that allows employers to voluntarily determine the eligibility of prospective employees to work in the United States.”
The Department of State confirmed that consular operations domestically and overseas will remain 100% operational as long as there are sufficient fees to support operations. However, this is only expected to last for a few days, after which consular posts will focus solely on diplomatic services and emergency services for American citizens. We expect delays in processing visas, and if there is a prolonged shut down, we expect a cessation of visa processing. During previous shutdowns, business reasons have not qualified for emergency visa processing.