The "idle stop screw" (located approx the center of your pic) can sometimes be difficult to adjust.

Often this is because the rotating part of the carb is stopping it. If you want to screw in your idle stop screw a bit, try holding the throttle open, and then turn the screw. Once you release the throttle, the opening should now be larger.

Also, some engine manufacturers use a bit of thread-locker on the idle-stop screw. Not loc-tite, just the gummy stuff. Guess they feel the spring isn't enough to keep the screw from vibrating loose. Anyway, this can make adjusting the screw more difficult.

All in all, I doubt your carb is broken.