Fat Tuesday is the classic frozen drink stop on the strip: when you see people carrying around the gigantic drinks, they are from Fat Tuesday or another place like it. This particular location is outside on the east side of the strip, close to Outback. It's lines get a little long, so the staff is pushy. They want you in and out.
I would not recommend getting one of the mega sizes. Some of the drinks are mostly frozen sugar. (Peach Bellini). Stick to a smaller or medium size, get the classic frozen margarita, and add a shot of tequila. You'll get more bang for your buck and feel a lot better than you would if you drank the three foot tall drink.