I thought that model ski has two carbs?
Well anyway, you can check your accelerator pump operation by looking straight down into the carb throat(use a mirror and flashlight?) while operating the throttle you should see(and hear) a good amount of fuel squirting out of the accelerator nozzle as you squeeze the throttle lever. After a few squeezes there won't be much fuel remaining in the carburetor chamber that feeds the acc pump, so pay close attention while watching the first and second shot.
Assuming it's a lean condition, you might also double check the low speed mixture screw settings, to make sure they're set properly. If they're too far in, you might experience a flat throttle response in the low end.
It's also possible instead, your mixture is too rich. If by pulling the choke briefly while the engine is stumbling, it suddenly perks up, that would indicate a lean condition exits but in the case it's too rich, the poor low end operation you describe can be caused by too much fuel as well (too rich), in which case there may be fuel leaking past the metering needle seat in the carburetor. Often when this is the case, the engine will also be hard to start from a hot shutdown as well, b/c fuel will continue flowing into the intake when the engine is not running.
Too rich? Since the engine doesn't immediately fall on it's face and quit when you open the throttle, this issue you describe could be excess fuel, which takes a few seconds to clear out through the cylinders once you open the throttle. Usually you would experience a rough idle, and could probably smell more than the normal amount of gasoline from the exhaust, maybe enough to quickly irritate your eyes.
Sometimes similar issues can be caused by near fouled spark plugs as well, try changing them if you haven't already. Think about when the problem first occurred, was it right after adjusting or changing something? Could be an air leak at one of the fuel line fittings, or the fuel/water separator cup o-ring isn't sealing.
Just a few more ideas of things to check for...