Has it entered "Shipping Soon" phase yet? If it has, then they're getting ready to ship it out right now. It's possible that they might be overnighting the game to you. If you don't get shipped notice by tomorrow evening, contact Amazon CS to see what is going on.
As for delivery on release date, it's more of a promise that can't sometimes before filled. As sometimes the warehouse your order ships from gets the game in late.
Also it seems Rockstar is pissed that Amazon broke street date and shipped it early to some customers who got it last week. So they might be withholding shipping up until the last moment.
This. And in the past, I've been worried, and many people told me not to. In this span, I found out (this may only be my area, but who knows?) that Amazon can mail it as late as 8pm local time, and have it on your doorstep the next day (this is usually only for Prime customers, or customer service issues). As long as it gets on the plane the night before, you are good.
EDIT: I had a Prime membership, which updates to release day shipping to any game they offer it on, even if not available when you order. I would order games 1 year or more in advance, and let it auto update to RDD. Sometimes Prime had expired, and they still upgraded the shipping option when it became available. In every case that I ordered a game that had, or eventually had, Release Date Delivery while I had an active Prime mebership (even if Prime expired well before game's release), the game was delivered on release day. I have had problems with damaged boxes, etc, but always got the product, so you should be good, man.