OK, so I now have it to the point where it will run. The fuel lines all checked out and I bled some air out of them to make sure they were not a problem. I also hooked a tube up to the carb and blew into it to make sure that there was a good passage-way for the gas - there is. So it is running now, but not really good. Here is what it does:
It idles just about right, but once every 10 seconds or so, it misses and you can hear the slack come out of one of the rods in the engine (a little "tink" sound)
If you hit the throttle hard, it revs up good, but backfires just a hair on the way back down (not a full backfire) but usually, it won't come back down to idle speed - it comes down to 2 or 3 times as high as idle speed. In order to get it down to idle speed, I have to just give the throttle a little "blip" and then it comes down to idle speed where it continues to run, but misses occasionally.
One thing of note here - the o-ring on the air/fuel mixture screw is actually broken. I did just throw it back in there with the break in it and I figured it would work fine that way, but maybe I was wrong? Any other thoughts?