The USPS won't refuse Basic packages from UPS. They receive a lot of money from UPS for deliverying these pkgs. With a multi billion dollar deficit, they won't reject revenue sources. (Before anyone says my particular post office rejects them.. I know that there are some rogue postmasters who have issues and do reject them, but they are the exception). For closing post offices, this won't be a major impact. The customers get a file quarterly, that lists the address a pkg should be addressed to for the USPS. So if zip code 01001 had a post office at 1 main st Clarksville, but then it gets closed the pkg for consignee at 01001 may have that pkg delivered to the USPS at 22 main st East Clarksville 01002.
The more concerning item is if the USPS goes down to 5 days\week, and they stop delivery on a Tuesday as they indicated before. That will cause issues to our customers.