There have been others that have done some long trips on this forum and the other motored bike forum. I don't think anyone has actually rode across the whole country. Look under Travels, Adventures and Touring section of this forum. http://www.motoredbikes.com/forumdis...Motorized-Bike
People ride across the USA every year on non-motorized bicycles. So, it could be feasible to ride a motorized bicycle.
With the limited touring experience I have with a non-motorized bicycle, you are going to need at least an additional 100 lbs or more of gear (tent, sleeping bag, stove, clothes, water, food, spare tire, tubes, sleeping pad, cooking utensils, tools, etc). And that's without a trailer.
A motorized bicycle would require additional equipment in addition to the previous mentioned gear (gas, oil, spare engine parts, etc.). If you add a trailer, you going to add more weight.
You didn't state what engine or what type of drive train you plan to use. You also didn't state if you were going to pedal assist or just use the engine for your power.
In my opinion, I don't think most of the engines that we use for motorized bicycles are durable enough without utilizing pedaling assistance - A Lifan clone (70cc or 110cc) of the Honda 50 motorcycle engine may be an exception. Running the engine all day at full power is definitely going to shorten the life expectancy of the engine. A 66cc/80cc Happy Time/China Girl would not be one of my choices of engines. I think you'd be having to carry too many spare parts and spending too much time on maintenance. If time and money are not a problem then go for it, but not my choice.
Do your research and look at what others have done. Definitely do several long trips before you start on your epic journey to work out the bugs. A network of contacts for spare parts would be a good idea.
Here's a blog of someone going across country and heading to South America: http://thirstybike.org/