Assuming you are talking about a rifle (since handguns cannot be shipped USPS) ...
Go back to the post office, and demand to speak to the local manager or post master. After you have pointed out that his employee was rude, demand that he open up his copy of the Domestic Mail Manual (DMM) and check section C024, paragraph 3.0
It essentially says that mailing long arms is okay as long as the rifle itself doesn't violate federal gun laws, and it complies with DMM C024 1.2 (i.e. non-concealable) and DMM C024 1.1e (i.e. barrel 16" or longer).
Also note that they are NOT allowed to mark the package in any way indicating the contents (but they ARE allowed to open it there and inspect that it is unloaded, before shipping it).
The law (and their regulations) do not state that you have to show them the FFL, but it might be a good idea for you to bring it, just in case.
However, be warned that USPS is usually far more expensive for a package that size than UPS. You'll often pay about $30 to ship a rifle USPS, whereas UPS would ship it for about $15. However, some UPS places will not ship firearms, and force you to go to their local hub, which can be a pain in the ass. (Unless you don't tell them what it is - not doing to with UPS or FedEx doesn't violate any law, just breaks company policy).