-Drill bit set (The more the better)
-*3/8" bit
-*1/4" bit
-Glue (Acryllic super glue or epoxy)
-Piece of plastic pipe/rod close to 3/8" OD, 1 inch or more in length
-The complete, original pump
Fixing a broken pump

So what I did was take a piece of ~3/8 OD hollow plastic rod, and jammed it into the pump. You can either sand down the plastic rod or take a drill to the interior of the pump, or both. Drilling the pump is a good idea- it's broken anyways, and it will mean more material for the strength of the inner rod. When it just fits smoothly, it is time for the glue. If you are using epoxy make sure it's a bit looser so that there is room for the epoxy to spread. Push the rod in quickly and get it into place before it gets stuck.

Do one end at a time, making sure to maximize the surface area for the glue. Hold the shaft straight and let the glue set for several hours.

Then carefully drill a series of small holes in the plastic rod, in the center of the old hole until you get up to 1/4". This should fit smoothly inside of the pump handle. I tried 7/32 but it was too tight and broke the inner rod the first time. So go for 1/4".

You can see the rod inside the pump.
And done. The pump is now fixed. It's been used quite roughly and so far so good. You could also do this proactively to reinforce the pump, just make sure you have a hammer handy to put the rod in all the way. Drill a hole in the rod and you are done. Now if only you could buy strong plastic rods from somewhere. The piece I used was from some broken gardening framing thing.
*EDIT* You can use a piece from a plastic coat hanger. Just cut it to size with an exacto knife/sand it.