As long as the oil spinner has been cleaned recently (first cleaning is due at 600 miles, according the the old manuals), you change oil regularly and the carb is in good working order, you're not going to hurt it, let alone wear it out, any time soon. You should be able to ride essentially flat-out until the tank runs dry. In stock form, it's an "unstressed" engine. Circa 2003 there was a widely-circulating blog covering two riders traveling along the entire western coastline of both South and North America...on Cub 50s. They made it.
The biggest hurdles you're going to face have to do with the vast amount of acreage we know as "the lower 48 states" (draw a 1K mile radius from where you're going to ride and you'll find very few major cities) and roads with speed limits that are friendly to a 35-40mph stock bike. The two conditions combined make for one tall order. Best of luck to you. This could be quite an adventure.