56 Imperial Carb Set Up

I just got my 56 Imperial home from the shop today after an extensive restoration. It was there for almost 2 years. However there are some minor glitches that I need help with. At the left side and slightly to the rear of the carb (assuming you are sitting in the driver's seat looking forward) is an assembly composed of a rubber diaphram, spring, idle set screw, and the main throttle linkage from the foot pedal passing through and attached to the right side of this assembly. What the heck is this doo hickey called? What is the impact if the rubber diaphram is cracked? It is cracked and you can easily see the spring just underneath. I can't see any vacuum lines running into this unit. In any case I am having trouble getting the engine to go to a slow idle even with the idle set screw backed right off. The return spring is plenty strong enough. Engine was completely overhauled along with the carb however the unit I am refering is not attached directly to the carb so was not overhauled.