If you own anything with a small carbureted engine, 98% of the time it's a carburetor problem. I just went through this last weekend right in front of the ice storm. The smallest - and I mean, the teeniest tiniest little piece of debris in a jet can make it not start or run poorly. If you don't need this generator right away, order another one on Amazon. Either way, get some carb and choke cleaner and always keep some on-hand. Remove the carb take everything out, keeping track of what went where and which way it was oriented.
Spray every part on the inside and outside, and you can even spray some in a glass jar or bowl to soak the parts that meter fuel. Now, get a thin sewing needle, a heavy piece of stiff fishing line, a twist tie with the plastic removed, anything that will fit inside the carb jet holes and all other holes, to clear them out. Be mindful not to get carb and choke spray on any gaskets or rubber o-rings, it will eat them away.
It's a good idea with a generator to have two carburetors - one for the generator and one for the shelf that has been cleaned (and possibly rebuilt) to swap out, and keep them in rotation. Then this situation is easily remedied. Whatever you do though, if you don't plan on starting it up again within a week or so, shut the motor down by cutting the fuel off and starve the engine to make sure no fuel sits in the carb. And also you may want to drain the title bit of fuel left in the carb bowl.