In my experience, let say you ordered stuff on Sunday with 2-day shipping, with estimated delivery date on Wednesday, they did not ship out on Monday and ship out on Tuesday, they will automatically speed up the order to overnight. and if you did not get the item on Wednesday I think you can get $10 promotion credit and 1 month extension of Amazon Prime
Qualifying for a Prime Extension under the GuaranteeSource [amazon.com]
Amazon Prime Free Trial and Annual Members can receive a free 1-month extension when the promised delivery date is not met. They will also receive a refund if they were charged for upgraded shipping. Extensions are limited to 1 per free trial and 12 for an annual membership. Note: Free Amazon Student and Amazon Mom Prime Memberships do not qualify for this extension.