NPR points out:
Since a new process was put into place in 1976, the U.S. government has shut down 17 times [Update: Make that 18]. Presidents Jimmy Carter and Ronald Reagan each dealt with six shutdowns during their terms in office, lasting anywhere from one day to 2 1/2 weeks.
The last actual shutdown came in 1996 …. The last shutdown lasted three weeks ….
This is not to say that there a shutdown would have no effect … but it is not the end-of-the-world scenario which some would paint it to be.