The linkage connected to the throttle and the spring are attached to an arm that should move. The arm is connected to a shaft that runs inside of the engine.
There is a proper way of adjusting this governor arm by loosening the screw and holding the throttle open 100%, and then tightening the screw. That adjustment doesn't always work, though.
You can try messing with it a bit until you get the right idle RPM that you want. The idle screw on the carb is used to fine tune the idle, not to really set it 100%.
When I messed with adjusting the governor on a 6.75 Tecumseh last week, it took just a few minutes until I reached an acceptable RPM (at least I thought it sounded good! It also ran good.)