Actually, they're not Federal employees (but they do still get really good benefits).
While the USPS may deliver 365 days a year, I don't think they do same day delivery and I don't think there's any way to actually mail anything on a Sunday. I mean, sure you can drop it in a mailbox (heck, my local PO building is open 24/7), but there's no way to process special treatment mail on a Sunday - nobody will see it until tonight, at the earliest.