How old is this machine? It might have gum deposits in the carburetor. If this is the case, try some gum-out in the fuel tank. It takes about 2 hours of operation for the gum-out to work, the result will not be instant. However, the gum-out will go everywhere in the carb, including internal passages that you cannot reach with a spray cleaner. If your snowblower has a valve in the fuel line, its a good idea to close the valve when you are done, and allow the engine to use up all of the remaining fuel in the carburetor, until it stalls out. This should keep the carb from gumming up.

See if it runs with the gas cap off. It's possible the cap is not venting correctly.