I worked on mine the day before you, and lost my spring. After searching for 3 hours and giving up, I found it. I can tell you that they do run without the diaphram spring installed...funny how I know that.
The only way that I have found that you can get a new spring is with the whole needle assy.
I think that the needle needs to be able to move a little bit. This helps in to find its home when the throttle is closed.