In the event of a federal government shutdown, the Postal Service will continue normal operations. However, “Passport Day in the USA” events scheduled tomorrow at more than 1,600 Post Offices nationwide will be cancelled, if there is a government shutdown. The Postal Service will NOT be authorized to accept passport applications.
As a self-funded independent agency of the Executive Branch, the Postal Service does not shut down if a government closure takes place. Employees are expected to continue to report to work. All delivery and mail processing operations will continue as usual.
In addition, Post Offices and postal facilities will remain open during normal business hours, with the possible exception of units located inside federal office buildings. In those instances, field Operations will inform these facilities of their operational status.
Employees also can check the status of their facility by calling the USPS National Emergency Hotline — 888-363-7462.
In the event of a federal government shutdown, click here for a printable poster explaining USPS facilities will be open for business as usual. Place the poster on all customer entrance doors and employee bulletin boards.
source: USPS News Link