I still think every time the government threatens a shutdown workers should start organizing to threaten a general strike. If the government saw union leaders organizing to strike once the government shuts down, they'd never let it shut down again. Exploit their weakness, if they want to stop governing, we should stop making the capital their owners desire.
Id wager most government workers wont need to strike during a government shutdown as most government jobs won't be functioning during the shutdown, they could march with the unions easily. The cops will be the largest group of gov employees still working and we don't wanna see them at the marches anyway.