Why should government workers be paid back pay when they return after a shut down? When I didn't show up for work, I was not paid.
There are 2 type of categories for .gov workers: essential and non-essential.
Those deemed essential even if the .gov shuts down will report to work on Monday and continue to do their job.
They will clock in as normal and do their 8 hour shift. However until the .gov "opens" again they will not be paid but will be due their wages for the work they continued to perform. Basically they are working 'under contract' and will be due money. Should congress not pay them they have legal footing to sue for payment.
The non-essential workers will report for 4 hours on the next biz day which in this case is Monday and will shut down all their stuff and then go home. They will not report back to work until the .gov opens again. It is this category of worker that congress may or may not pay for their time away from work depending on when the .gov opens up again. In prior .gov shutdowns, congress has paid this group anyways as they had no choice but to not work.
The next question I'm sure you will have it if they are 'non-essential' then why have them?
Non-essential is just the term used for those workers an agency has that do not focus on the agency's mission per say.
For example in the VA a .gov doctor is considered essential as you need a doctor at the VA. However the IT guy is not essential to keep a patient alive. He is non-esstential to the mission of the agency. But it is cheaper to hire an IT guy then it would be to contract out that IT work. Cheaper does not always mean money. It could be due to security reasons (ie. sensative files, etc..).
So while the VA could continue to run without the IT guy. Eventually you will need IT support.
Same concept with other agencies. Think the facilities people who maintain the building or HR people, or public relations, etc. Most of these functions do not focus on the agency mission but are support type which keeps the actual .gov worker going.