The phrase generally means to find a path through two opposing views. It's often done by politicians who try to have their cake and eat it too.
When you hear or read "thread the needle" it means take the end of the thread and push it through the hole in the needle. There are several different methods of threading the needle. You can find three here: http://needlepoint.about.com/od/toolsandsupplies/ss/needlepoint001.htm
In reference to "find a needle in a haystack" you increased precision to the point that you could not only find the needle, but you could thread it where it laid.
In WWII a pilot had trouble finding his target much less when he did see it, for the bombardier to hit it, so we just mass bombed areas, often the only thing remaining in the town was the target. With improved navigation and bombing they were able to fly to a precise spot and drop a limited number of bombs. They were able to find the needle at 45,000 feet, and so to speak, thread it, or fly through it, or put a bomb down the stack (smoke stack).
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