This is extremely common for a Verizon preorder. Their system gives out guesses.
My guess is if you preordered the night of, and got a 16th delivery date you'll probably have it in hand on the 16th.
Verizon has hit their dates every single year in deliveries to us when I stay up late.
I ordered mine around 9am on the 9th. I went ahead and went with the 128gb rose gold instead of the 256gb because it was saying deliver by 16th. My confirmation email says the 16th too, but when I click the check your order status it's been saying ship by 28th since late Friday night.