The expression itself irritates me. Truncated as it is, it makes no sense. The phrase is “to make a long story short.” That actually has some meaning.
I used to hear the full expression used when someone really was abbreviating a tale, omitting a lot of detail and skipping middle parts—making a long story short (that is, shortening the story). Now I think it is itself just more empty filler, uttered mindlessly because (nearly) everybody else does.
Either that or it’s a half-hearted apology for going on at length and now the speaker realizes he’d better hurry up or he’ll lose his audience, and so he tells you he’s finally going to wrap it up. In this use it has the spirit of “bear with me.”
You’ll never hear me say it.