This could easily circumvented by passing the Stop STUPIDITY Act, which basically says if the government can’t pass a budget or continuing resolution in time, the government automatically adopts the previous year’s budget and suspends all pay for the legislative and executive branches until a new budget is passed.
Instead of using government workers keeping intact our very thin veneer between civilization and barbarity as bargaining chips at best and hostages at worst, the pain would fall squarely on the President and Congress.