If you have the 2000i model, here are a couple of alternatives to correct your problem. These may also apply to the 3000i model too.
- Remove and clean the carb. Here is a file I saved from RV.net long ago on the process. It is very complete and comes with pictures. Honda 2000 Carburetor Rebuild Instructions.pdf
- Buy a replacement carb off of Amazon and other sources for $25 to $35. A quick and easy way to cure the problem. Here is a sample link. https://www.amazon.com/Honda-Power-E...40065403&psc=1