Tank, as bigted said, we need the Type as well as the Model to point you toward the Illustrated Parts List and Operator's Manual. Meanwhile as far as I know, all 281707 engines use the large one-piece flo-jet carburetor. The symptoms you have described sound unusual, but as bigted said, the first step is to remove the air cleaner and see if that makes a difference. If it does, the air cleaner is clogged and needs to be cleaned.
The large one-piece flo-jet is about as reliable a carburetor as can be found in the world: the nearest thing to a characteristic fault is that after about 20 years' running they sometimes have suffered some wear to the needle and seat, which then require replacement. You can read about this in some detail in the following thread:
https://www.outdoorking-forum.com.au/forum/ubbthreads.php?ubb=showflat&Number=15306You will notice that the symptoms Nathan reported are a bit different from yours, depending on how we interpret your reference to hunting, which normally is caused by lean mixture, whereas most of your symptoms sound like rich mixture. There are simple faults which can cause mixture to be alternately rich and lean, in particular a sticking float lever in the carburetor float bowl under the needle. However, please post the engine's Type, and also report whether the carburetor floods when left for 10 minutes or so with the fuel turned on (see the other thread referenced above, for details of what flooding is, and how to detect it).
This problem should be simple to find and to cure. We just need to all be aware of the detailed symptoms, and background facts like whether the machine has been left parked with the fuel turned on. (Incidentally, never do that. Sooner or later the carburetor will flood, resulting in a large amount of petrol ending up in the engine's lubricating oil, with very unfortunate effects on longevity.)
