According to Jabsco's propaganda sheet, it will self-prime a little over seven feet vertically. That of course, is if it is in tip-top shape.
If there is some residual water in the lines, it will draw that out before you get a smooth flow of water. But what I'm getting from the way you worded you question is that you aren't getting a smooth flow at all, and that it's spitting and sputtering. If it's doing that, you've likely got a bum diaphragm in it.