When I've run into this issue, it means the air bleed for that side is plugged. I clear it up by removing the idle screw (keep track of the little seal!), and giving the circuit a few short blasts of compressed air. Then I do the same back through the air bleeds, which are the tiny tubes poking out of the top of the carb.
This isn't to say something else isn't a problem, but it's an easy place to start.