Almost all of the bishops who attend are from the East, and the western churches will be slow in accepting it as genuinely ecumenical. Ultimately it will be, though, because of the orthodoxy of its pronouncements.
Another problem is the early refusal of Pope Vigilius to attend. Even though he is in Constantinople, he opposes the hard line the council is expected to take and forbids such a council to meet without his presence and approval. The council, however, doesn't recognize any such authority in the pope and proceeds to implicitly excommunicate him until he submits to Emperor Justinian's demands.