In most cases, you'd probably make the employees at whatever agency or department very unproductive for the next few days (or however long it takes to find the server and plug it back in). The kind of projects I'm talking about are usually internal and critical for getting the right data to the right people within an agency.

So its is not critical from country/world perspective...

At what point does something become critical, in your book?

The kinds of services I'm describing are critical to the normal functioning of government agencies. They're running now, and they'll probably be running for the next 25 years (at which point another contractor will upgrade them to something new and shiny).

When problems/lack of it influence life(life != work) of many people.

- If power grid goes down you are facing riots.

- If systems on your new shiny Boeing go down you are facing deaths of dozens of people.

- If your military systems goes down you are facing russia ;)

If employees of government agency works less efficiently(is it even possible?) for some period of time (few days, months?) - nothing wrong happens. That's why it is possible to change those systems every 25 years. They will be less productive after software change, they will face new bugs in transition period. A lot (but not all!) of work those agencies do exist only because of some stupid laws (example: in my country you have to have special permit to cut down a tree on your land - I know someone who had to start building their house year later because they couldn't get permit to get rid of one tree, another one: you cannot inherit some types of parcel if you are not a farmer - you have to either become farmer[of course virtually - but it takes few months] or change parcel's type [it's not always possible and it's also few months of fighting with bureaucrats ]).

Depends on the government agency I'd say. For example: unemployement or social security checks going out, VA Hospital systems, etc.