In the 17th century a group of Scots attempted to found a colony in Darien, with disastrous results. As well as most of the colony dying, it bankrupted Scotland and thus led to the formation of the United Kingdom. Plans for Darien have had much the same level of success ever since...
The Darien Gap is the one break in the Pan-American Highway, meaning that overland travel across Central America is pretty much impossible. This 60 mile gap without roads has been successfully crossed a handful of times - usually by expeditions equipped with off-road vehicles and staffed by special forces types. Attempts to bridge the gap with a road have stalled, because of environmental protest or concern that an overland route may expose North America to foot and mouth disease from South American cattle.
Finally, did we mention the three Colombian rebel paramilitary groups who operate in the area? It doesn't sound like an easy place to visit.
Crossing by a combination of foot and boat is not only possible, but easy. Stick to the Caribbean side and "hedgehog" from resort to resort.