The package the next day will say "What is this?", and your only option is to open it. If you still have the package unopened in your pocket, and talk to the villager that wanted you to deliver it, they will either be sad or mad and taken it off your hands. Slightly decrease friendship level. However the villager that the package needed to be delivered to, will never know and won't think anything of it, even if the package is now "What is this?".
It's only the villager who wants you to deliver it that has a friendship decrease if they see it undelivered the next day. You gain more friendship if you deliver it to the villager and tell them. The villager receiving the package can only get a friendship increase in this situation, delivering it and friendship increases, not delivering it they will never know.