I wouldn't worry about it for at least three days, since of course a package dropped in a deposit chute on Friday might not even get looked at until the following Monday.
Realistically, I have not seen any clerk ever look at the print date. The shipping date is whenever the package is scanned as Accepted.
On the other hand, once you receive clear payment, your Shipping clock starts, and it doesn't stop when you print a label; it stops when your package is scanned as Accepted. So don't worry about exactly what date is showing on the label, but just get it on its way as soon as possible.
