How about put some of that fuel stabilizer in it. Well the new carb or rebuild would be better but just thinking a quick simplle fix. I am such a believer of bad gas now. When i bought my pressure washer brand new, and left it for two weeks with gas in it. I went to start it and it was smoking and would only run for about 10 seconds. Like yours. This was a brand new Honda engine. I put new gas in it and it purred like a kitten. No smoke