The two hosts of the radio programme El Vacilon de la Manana (Morning Joker) spliced together clips from a Chavez speech and played them to trick Mr Castro into thinking he was talking to the Venezuelan leader.
"What we don't want is to create some vague prospect in the future that somehow comprehensive immigration reform that includes a pathway to citizenship will happen, you know, manana, " Mr Obama said, using the Spanish word for "tomorrow".