I was making a joke.
But they don’t guarantee that as part of Prime.
I’ve never had trouble like “order Monday, processes Tuesday, so you get it Thursday” on a truly Prime order. If I order it on Monday during reasonable business hours, I have it by some time Wednesday. Basically it’s always 2 business days. If I order it Thursday, and Monday is a legal holiday, I get it Tuesday since Monday is not a business day.
Now, they DO have a new deal with some third-party “Prime” vendors where it may take longer because the vendors were complaining about the burden. I avoid those items as a matter of principle.
I’ll say this… since they stopped using UPS/FedEx as their primary delivery services, the variability in delivery times has gone way up overall for Prime items.
Their own drivers are frequently showing up later in the evenings than the big delivery services used to, or packages get lost, etc… and whenever they involve the USPS, it’s a total crapshoot as to what will happen to your delivery.
I had nine Amazon Prime deliveries in January, all of which were shipped USPS. Seven arrived on schedule, one arrived a day late and one was several days late because the mailman initially delivered it to the wrong address.
A 78% success rate - that’s a solid C! Nice work, Amazon!
I did have a new experience the other day. Doorbell rang and I heard something being set on the front doorstep (common here, and theft has not been a problem). I opened the door to grab it, and a driver wearing a bright yellow safety vest was getting into a car - looks like they/re contracting SOME of the work out to people driving their own vehicles now. 
what annoys me is when they use ups up til it gets to about 50 miles near me and then it switches to the post office and takes an extra 2 days as usps sorts it out …
That’s “smartpost” or something like that. Basically UPS uses it to get to a USPS facility fairly close to you, and then lets them handle the actual delivery portion.
Smartpost and its ilk are the most awful delivery schemes anyone ever thought up. It basically takes twice as long, and introduces 2x the points for error to creep into the system.
Regarding smartpost, IME it usually still makes it to me within two days (or at least it does now). However, I’ll still contact Amazon if it doesn’t. If FedEx/UPS delivered it to USPS by the due date that’s sort of a “and how is that my problem?” thing.
Same with when I was having an issue with Amazon saying something would be delivered to me on Sunday, then, it would say it was out for delivery, then a few hours later it would say “Could not deliver, business closed today, retry tomorrow”. I’d call up Amazon, they’d parrot that back to me, I’d explain that we were, in fact open. They’d suggest that maybe we just appeared closed and I’d explain that we’re a store, a very busy store, perhaps the mailman just couldn’t find a parking spot and kept driving. In reality, they probably just saw that it was a business and never even came near us.
I think that happened two or three times…now all the Sunday deliveries show up just fine.
Worked out well for me, I got a few extra months of Prime because a box of paperclips or something showed up on Monday instead of Sunday.
I don’t have Prime but deliveries out of SoCal and Arizona are often delivered by OnTrac.
It may have been a local courier service, most do small packages.