According to the World Run II website, Jesper will resume running in Key West, Florida and hopes to reach the Canadian border by mid-April. After a short break, he'll then run New Foundland, reaching the end point sometime around early July. The total distance for the North American section, a mere 5600km (3479 miles). When he's done, Olsen will have completed the longest fully documented, and GPS tracked, run in history, which follows-up his World Run I, which saw him covering 25,000km (15,534 miles) as he circumnavigated the globe.
Entering North America is a major milestone for an excursion like this one. While the physical demands won't necessarily get any easier, the infrastructure is much improved, allowing athletes like Jesper to follow clearly marked routes, find food and accommodations much more easily, and generally proceed at a better pace. While he isn't quite done yet, it does appear that Jesper is about to start the home stretch of his expedition.
Thanks to Darrell for keeping me in the loop with Jesper's progress.