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Your best bet is to clean out your carburetor.
First turn of your fuel or pinch off the fuel line.
Turn you machine on its snout so that the handles are facing straight up in the air.
On the back of the engine you will see the carburetor float bowl with your main jet in the center. (You may need to remove the belly pan) Remove this jet by unscrewing it and gently remove the bowl inspecting to see if there is any debris inside it. Clean the bowl and spray some carb cleaner straight up and into the hole the jet was unscrewed from.
you will also need to clean the jet thoroughly including the little hole not just the big one (see picture) Once everything is clean set the machine back on it's wheels and turn the fuel on allowing fuel to run through into a drip pan for about 10 seconds.
Stand the machine back up and reassemble. This should get you going.
Thanks for the follow up, almost forgot about you. I followed your instruction to the letter, it still does the same thing. But I did discover pumping the primer bulb when at an idle makes a big difference, fuel filter plugged?
Most likely you still have a clog inside your carburetor. Priming it is just increasing the fuel to air ratio, which is what your jets are supposed to do. Snowblowers do not normally use a fuel filter. At this point the only real fix is to remove the carburetor, disassemble it and then soak it in a commercial carb cleaner overnight and then rebuild it with a new carb kit.