Most likely there is some kind of obstruction in the fuel system that will not allow enough fuel to get to the cylinders. Start at the tank and loosen the fuel cap. The vent may be plugged. Proceed to the carb and remove the fuel line. There should be a steady stream of fuel flowing out the line about the size of a pencil. If not, the fuel line is clogged between the end and the feed at the bottom of the tank. Check inside the tank for debris blocking the hole going to the sediment bowl/shutoff valve. If there is good flow to the carb, the carb needs cleaning or rebuilding. There are rebuild kits available from several sources, possibly even this site. Berrymans B-12 is the best carb cleaner I have found yet. You can simply fill the fuel sediment bowl with it and start the tractor. It will clean varnish buildup out as it passes through the fuel system. If this doesen't work, I suggest a thorough disassembly and cleaning of the carb, taking care to clean all small holes and passages with a small, stiff wire.
Other problems may be a worn throttle plate shaft allowing excessive air to enter, and deteriorated carb to manifold gasket doing the same.
Let us know how it comes out,