The only way you'll get it on the same day is if you order it early in the morning for evening delivery. It's not a local supermarket, they need to schedule a driver and bring the stuff to you from their warehouse.

Most supermarkets around me (NYC area) do deliver. Some for free. On top of that, there's Peapod, Fresh Direct, and a bunch of others.

This is a profoundly stupid move by Amazon. I can't imagine anyone would want to pay for this considering the alternatives available in most metro areas.