What does it mean for a government to be shutdown, and how does it affect the nation?
In U.S. politics, a government shutdown is a situation in which the government stops providing all but "essential" services. Typically, services that continue despite a shutdown include police, fire fighting, the National Weather Service and its parent agencies, the postal service, armed forces, utilities, air traffic management, and corrections (the penal system).
As mike points out only essential services, but it's only federal services that will be shutdown like medicare, social security, welfare etc., while solvent state and local governments will mostly remain unchanged. Each state or county will be effected depending on how much it receives/gives from and to the government, like DC's($5.55) economy is hit pretty hard compare to Texas's($0.94) economy. I also doubt services would be cut based on what's essential instead of what helps one politically.
Here's more data. Reference: http://stonesoup.wordpress.com/2011/06/07/federal-funding-received-by-state-per-dollar-sent/