For a while I worked at a post office. I feel much better now, thanks. While working there, I of course got to see how things worked. While there's plenty to notice and comment upon, I'll keep it to today's mail.
A mail carrier normally arrives at the post office early, around 6:30 AM and sorts through all the mail to be delivered on his or her route. Around 8:00, ideally, the sorting is finished and the carrier can go out on the route and deliver. If the carrier for a given route is unavailable, another person is called in to take the route. This person usually has been trained on that route and so supposedly knows any quirks of it, and might even remember them.
Most mail carriers work a six day week, so a Monday holiday like yesterday's President's Day makes for a somewhat rare two day weekend. The mail doesn't completely stop on Sundays and holidays. It's still collected from the blue mailboxes, at least some of them, and still sorted and sent through the system. So on the Tuesday after a holiday, the pile of mail each carrier has to deliver is larger than usual and takes more time to sort and perhaps to deliver as well. That's part of why today's mail will probably be later than normal.
The other part is that people like extended weekends, and if only takes one day of vacation being used to get a weekend two days longer than normal, then that's what people try to do. Mail carriers will try to get the Tuesday off after a holiday. This gives them a three day weekend. It also means the substitute carrier gets to deal with the larger than normal amount of mail to deliver. The result is that the deliveries go even slower as the substitute takes more time to sort through and arrange the larger volume of mail and also takes more time to deliver as the route isn't nearly as familiar as it is to the regular carrier.
There aren't enough substitute carriers available to call in for all the regulars to take off, so maybe your mail will be on time. Almost.