Why wouldn't the popes take this opportunity to declare a crusade against the Ottomans? Isn't this a prime opportunity to reunite the Catholic and Eastern Orthodox churches? Was there any political or logistical reasons why this couldn't happen?
There were mainly political reasons why the west could and did not mount any kind of attack on the Ottomans in 1453. While the Popes (in general) had been interested in reuniting the Western and Eastern churches, the Greeks had proven resistant to the idea. Prior to 1453, an understanding between the Pope and the Emperor had been reached at the Ecumenical Council of Florence in 1439, but the Emperor and bishops had failed to convince the eastern clergy to agree by the terms of the council. Moreover, there actually had been a crusade against the Ottomans that concluded only 8 years prior: the Crusade of Varna, lasting from 1443 to 1445, which ended disastrously for the Catholics, breaking the dynastic union of Poland and Hungary with the death of Władysław III.
During the Hungarian reign of Ladislaus V, the Hungarians did fight the Turks, but these were mainly defensive actions. When Ladislaus V died without an heir in 1457, he was replaced by the capable Matthias Corvinus, who spent a large part of his early reign defending southern Hungary from the Ottomans anyway. The other half of the former union, Poland, was now unified with Lithuania. At the time of Constantinople's fall, the Poles and Lithuanians were engaged in wars with the Teutonic Order for control of Prussia and Livonia.
Further to the west, the Kingdoms of France and England (and to a lesser extent, the mostly-independent Duchy of Burgundy) were engaged in the terminal phases of the Hundred Years' War, which trumped any real interest in crusading that the rulers may have had until their domestic situation was more secure. The Iberian Kingdoms were engaged in the reconquista still, effectively their own crusade much closer to home. Northern Italy was still embroiled in conflicts in Lombardy involving most of the major Italian states.
The popes during and immediately after the fall of the city were actually quite interested in mounting a military effort to recover it: Pope Nicholas V tried unsuccessfully to organize aid to the city and after its capture tried to organize a crusade to retake it. His successor, Callixtus III, also attempted to organize a coalition crusade to push back the Turks. In both cases, the local military and political considerations of the western states trumped any interest in committing to a crusade to the east.