Most of the government employees I know feel it's an honor to serve their country and do so with loyalty and pride. In past shutdowns, they've all gotten paid retroactivly. It's not always about money.
That's strange, most of the ones I know do so with frustration and resentment. Perhaps you're referring to a different, more amicable government?
It's not really up to them, though.
Folks deemed "essential" like security screeners, the Coast Guard, etc. are expected to still come to work. Non-essential employees are furloughed, and it's actually illegal for them to volunteer their time.
https://www.usatoday.com/story/news/politics/2013/09/23/gove...
> Natter noted that the Anti-Deficiency Act, the 129-year-old law that forces the government to shut down without an appropriation from Congress, also makes it illegal for furloughed workers to volunteer — even though many end up getting paid whether they work for not. "It really ought to be rewritten to be more relevant for the 21st century," he said.