let the gov shutdown, lets see those stock prices tumble. You'd never get a better chance to let republicans shoot their own donors in the dick. Lets see spacex stop getting checks, stop paying the supreme court. The rule they're using to "shut down" the government is likely unconstitutional anyway.
The shutdown would be triggered by Congress not passing a funding bill, something that's happened 3 times since 2013, and the supreme would continue to get paid if this happens.
It seems like the supreme court staff would all be furloughed though. Could probably cut power to the buildings too. With a little creativity they could certainly create a situation where the supreme court stops getting paid and there is no way to convene the court to deal with it.