Sorry to hear about your troubles.
The simplest solution is to just replace the carburetor. That way you know the problem will be taken care of.
The carburetors can be cleaned, and it is not too difficult to do so. The caveat is that if there is a gross buildup in hte internal passages, cleaning may not be sufficient.
The parts can be obtained from most any small engine shop. You will need the brand and model number of the engine, and the model number of the generator would be a good idea. It should be found on a tag attached to the base of the set somewhere and should look something like PM0525300.
If you are not near a small engine shop, you can call Pramac (the maker of PowerMate) directly at:
For Powermate Parts, please contact:
Toll-free number:(NNN) NNN-NNNN
If you have the engine make and model, there are several polaces online that you can order from:
as well as many others.