Two laws needed to hold Congress accountable to the People.
First, Congress needs to pass a balanced budget by 1 October every year, or they don't get paid. So if 1 October comes and they don't pass a balanced budget, then until such time as they do, they don't get paid. Furthermore once they establish the balanced budget whenever that might be and pay resumes, they don't get back paid for the time it took for them to actually do their job.
Second, if Congress does allow the government to "Shut Down" as it were. Then they forfeit the right to run for re-election until someone has sat an entire term in their seat. So again if they fail to do the job they were responsible for, they essentially get "FIRED" for an entire term.
The People of the USA want Congress accountable for their actions