Hi Ryan:
I'm new to this site as well. My brother and I recently ran into the same problem, except it applied to both a bit we were using in a boring machine as well as a t-auger. We found that the problem is definitely with the lead screw, as it draws the bit into the wood and if it's dull no amount of sharpening the cutters makes a difference as the lead screw clogs up and then does nothing.
First off, if you're boring into green wood, and especially softwoods, I suspect the thread needs to be fairly coarse (lots of space between threads), which it wasn't with the boring machine bit we were using. We couldn't do anything about the fine threads on the lead screw for the boring machine bit but we did succeed in sharpening it enough to make it work.
To sharpen the threads on the lead screw (which involved deepening them as well as bringing them to a sharp edge) we used what I've seen called a teardrop file: I think it's used for big old crosscut saws. At any rate, its cross-sectional shape is like a teardrop, and the fine edge fits between the threads and allows you to get in there. We sharpened the threads from the bottom (fat) part of the lead screw to the tip and found that as you got to the tip you naturally produced a sharper point. It worked, quite well.
There may be a better file than the teardrop one to use (no doubt there was a specialized one for the job). Leonard Lee describes sharpening threads in his book on sharpening, though I don't recall that he says a lot.
If you can find and afford a boring machine, do get one. It's faster, and easier on your arms, and more importantly, it gives much more accurate holes. Drilling a straight hole for several inches with a T-auger is quite a challenge.
Hope this helps.
Eric