The "Panama Hypothesis" states that the gradual closure of the Panama Seaway, between 13 million years ago (13 Ma) and 2.6 Ma, led to decreased mixing of Atlantic and Pacific water Masses, the formation of North Atlantic Deep water and strengthening of the Atlantic thermohaline circulation, increased temperatures and evaporation in the North Atlantic, increased precipitation in Northern Hemisphere (NH) high latitudes, culminating in the intensification of Northern Hemisphere Glaciation (NHG) during the Pliocene, 3.2-2.7 Ma. Here we test this hypothesis using a fully coupled, fully dynamic ocean-atmosphere general circulation model (GCM) with boundary conditions specific to the Pliocene, and a high resolution dynamic ice sheet model. We carry out two GCM simulations with "closed" and "open" Panama Seaways, and use the simulated climatologies to force the ice sheet model. We find that the models support the "Panama Hypothesis" in as much as the closure of the seaway results in a more intense Atlantic thermohaline circulation, enhanced precipitation over Greenland and North America, and ultimately larger ice sheets. However, the volume difference between the ice sheets in the "closed" and "open" configurations is small, equivalent to about 5 cm of sea level. We conclude that although the closure of the Panama Seaway may have slightly enhanced or advanced the onset of NHG, it was not a major forcing mechanism. Future work must fully couple the ice sheet model and GCM, and investigate the role of orbital and CO2 effects in controlling NHG.