Recent research tells us that, at its peak, Mayan civilization was a densely populated myriad of thousands of city states, comparable to the city states of classical Greece. My understanding is that overpopulation drove the Greeks to settle distant colonies all around the shores of the Mediterranean and Black Sea.
Did the Maya do anything similar? The isthmus of Panama seems climatically similar to the Yucatan, so did the Mayan culture reach that far?
This is tangential to your main question, but I just want to point out that overpopulation was almost certainly not the driving force behind Greek settlement overseas. Archaeological evidence suggests that there was plenty of unused land in most Greek states during the period of most intense overseas settlement; no contemporary evidence suggests that Greek states suffered population pressure, except in times of emergency (drought, crop failure etc.). You can read more about Early Greek migration in my recent post here.