It depends a lot of where you are located and where they are shipped from. How direct is the shipping, how many different shipping centers have to handle them? Most are shipped by air, is it a direct flight or is there a stop on the way? Are you close to a major post office sorting center or will they have to be trucked to a remote location?
I've had chicks arrive the morning after they shipped and some arrive two morning after they ship. According to post office regulations the chicks have to ship within 24 hours of hatch and shipping should take no longer than 48 hours. So unless their is a glitch in shipping they should arrive the next day or the day after that.
Humans are involved in transferring them so there is always a possibility of a mistake. Mechanical problems can ground or delay a flight so connections are missed. Weather can really mess it up, not just tornadoes or blizzards but severe thunderstorms. I avoid shipping on holidays, a lot of the complaints over shipping you see on here are over a holiday. There are a lot of things that can possibly go wrong but the reality is that the vast majority arrive within that 48 hour window.
Excellent. I don't know how often your local post office receives mail deliveries from the distribution center, mine was just once a day, a rural post office not on a major route. I would expect you to get another call tomorrow about the same time. Good luck with that one.