Do you think mortgage companies and utilities will actually accept?
In general banks and utilities will not accept carpentry or other labor in exchange for getting out of paying your mortgage or utility bills, because they have way more customers than they have demand for carpentry or other physical labor. Officials in the Trump administration should have known better and not suggested that as it wont work. The only useful advice to these workers is to have an emergency fund that will last through the shutdown and when it comes to public policy we shouldnt be allowing these shutdowns to happen on a regular basis as its going to be hard to recruit/retain talented workers if people know they wont get their paychecks on a regular basis. Most people go into government jobs with the expectation that they will be more stable than private sector jobs, especially given that salaries are often lower.