Tom,
If you can check the oil and have got enough coolant still in there to start the generator, you can look at the smoke. Maybe someone can check the fluids for you, topping off as needed.
If the oil looks diluted, since that unit doesn't have a oil cooler that I know of, it could be a head gasket. If you see a pile of white smoke, it could also be a head gasket.
If you don't see either, you've probably eliminated the head gasket as a possibility and can focus on less expensive and more common problems, such as the exchanger.
White smoke from the head gasket will tend not to smell bad or smell slightly sweat and rise up quickly, like the steam that it is. By contrast, white diesel smoke smells aweful, like diesel, and tends to linger lower rather than rising up as much.
Diluted oil tends to look milky.