I think that one of the reasons that the federal government fights a shutdown tooth and nail is not because they want to protect the American public but because they're afraid that they will shut down and the American public will figure out that they are better off. What better way to know what parts of government are truly important than to bring the whole thing to a halt? If the public doesn't notice that a particular office is not operating, then that office or agency just doesn't reopen. Easy and quick way to identify necessary budget cuts.
Over in Britain (England, Wales, Scotland), they had public sector strikes that pretty much DIDN'T succeed in shutting down the country. They were expecting long delays at Heathrow Airport but things actually moved along much more quickly--probably because the slackers are the ones who went out on strike and the good employees are the ones who showed up (approximately 60% showed). Hopefully those in charge will take note and will use this as a learning day--learning who and what is most necessary so they can cut the rest off the public sector payroll.