Postage Due - How does it work?

They are still hoping you will pay the extra 45 cents though. But, as aceplace notes, the postman’s time is more valuable. It is really just on the honor system. However, if most people just don’t pay the amount due, then the post office will be more inclined to just return to sender.
At Fort Benning, when basic trainees receive mail marked “postage due”, they also receive a litte paper envelope to put the change in. They are supposed to put the money in the envelope and drop in any mail box. It is basically a courtesy extended by the post office. If most people didn’t pay it, though, I’m sure they would stop doing it.
Sounds like you did not get an envelope to put the due postage into. If I were you, the next time I mailed a letter I would put 45 cents extra postage on it.