Here's a better idea than blocking ploiticians pay durring a shutdown (bacause that can be used to strong arm poorer politicians). If the government ever shuts down, funding continues as it was and we immediately hold elections for both the senate and house with all current members being barred from ever holding office again.

Some Dems at least made a show of trying to pass a law so they wouldn't get paid during shutdowns. Unsurprisingly Rs voted it down.