It's impossible to have only "essential" staff as you will always need "non-essential" staff to support their work. For example, NASA TV employees are "non-essential" [1] but without the TV station it may mean lots of kids are not inspired by NASA any more. Also, Labor statisticians are "non-essential" but would you rather the Department of Labor make decision on gut feelings instead?

[1] http://www.nytimes.com/interactive/2013/09/27/us/who-goes-to...