On your carburetor, is there a jet that looks like a screw that passes through the nut that holds the float bowl on? It should have a spring on it.
Has anything been done to the engine? Has it set up for a few months?
The float bowl is held on by a bolt on the bottom. I think I see the screw at the top of the bowl. Should I pull it out and see if it has a spring?
Nothing has been done to the engine and it has been runnign steadily for a month.
You have what's referred to as an "emissions" carburetor. It's preset from the factory in an attempt to cut down on unburnt hydrocarbons.
I think your assesment of it not getting any gas at throttle is spot-on. Probably what's happening is that the carburetor has a little trash in it which is either blocking the fuel flow to the venturi or the air flow into the bowl. What I would do in the shop for this sort of complaint is to remove the carburetor and give it a good soaking in a can of carburetor cleaner or in the ultra-sonic cleaner. This can be bought at any auto parts stores, it will come in a paint can sort of container and around here probably runs around $40. Spray cleaner might work, but it can't reach into the tiny air passages. You can try it though if you don't have a carb vat. Pull the float bowl off and spray the cleaner up into the carb and the fuel nozzle, or tube that runs through the middle of the carb body. If the screw that holds the bowl on has holes in it, make sure that they're good and clean.
You might also think about just replacing the carb with a new one if you have to buy the cleaner. By the time you buy the cleaner and a carb kit, you're pretty near what a new carb might cost.
As an alternative to the carb cleaner vat, you can try soaking it in distilled white vinegar heated to 150-160 degrees F for an hour or two. You'll need to rinse the carb off in distilled water with a few tablespoons of baking soda then again in plain distilled water. This makes an excellent cleaning solution, but you'll need to frequently turn the carburetor or agitate the vinegar somehow.
If you can give me the model and spec number off the engine I'll find you a price for a carb and the numbers for the kit. Then you could make a better decision.
I just gave it a rip without the air filter and it ran great. So although the filter looks clean I'll replace it.
That might be all you need. Was the engine smoking black before?
Usually a clogged air filter will cause the engine to smoke black because the fuel/air mixture is enrichened as a result of the reduced air flow. You may have caught it just as the filter is becoming overly clogged. If so, then a new air filter may be all you need. I'd also check the spark plug as it may be somewhat fouled as well.
If the problem persists, then I'd go through the carburetor. The carburetor part number is XXXXX and I have it listed at $65.95 which is probably about average. The kit is part number 632760B which I have listed at $12.50, which is also about average.
Hopefully a new air filter will resolve things.