The tubes are vents for the float chambers. Theoretically, if they were blocked, that would create a vacuum In the chamber and could stop the fuel flowing out of the chamber and into the carb body. The blockage could be in the airbox tubes, in the rubber pipes ( which may have been kinked) or in the top of the float chamber. Might be an idea to take the tops off the float chambers and see if there is any debris on there and make sure the needle valves are not sticking in the "up" position and cutting the fuel off. And there is no debris floating around that might have been blocking the fuel outlet and you cleared it ( for now) by blowing down the tubes.