They tried that on me today (I've had a bad run this month - I usually have about an order a day)...

Item bought on Monday, with expected -delivery- Wednesday. Late Monday status said "Package has left seller facility and is in transit to carrier".

It's Friday morning now, no package, and status is still "in transit to carrier".

I argued that "Shipped" means the carrier has it. Not that it may or may not be sitting in a corner of a truck for the last week forgotten or unnoticed.

Give them a link to the terms of service and say "please direct me to the language in your terms of service to that effect." Follow up with "as a paying prime member, I insist on compensation for Amazons failure to meet their guarantee". This has always worked for me. Some reps have pressed back when I insisted on two instances of compensation for one order with two late packages. I replied "I have no sympathy for a multi-million dollar company that fails to meet its obligations." Have gotten several months of prime and gift cards through chat in this way.

I've only done this via chat, I don't have time to sit on hold or deal with phone.