You have probably noticed that Amazon has pulled next-day and same-day shipping options when checking out in the weeks leading up to Christmas, presumably because the company's warehouses are drowning in holiday orders.
The good news is, there is a way around it. Your experience may vary, but it worked.
After you place your order, immediately click on "Your Orders".
(Do it quickly, you generally only have a few minutes at most).
Find the order you just placed, then click the "Change Shipping Speed" button.