It was important to ratify the Constitution as soon as possible because Article VII stipulated that nine states had to ratify the Constitution for it to go into effect. This is the reason why, when a new state ratified the Constitution, it was seen as a big accomplishment and widely celebrated.
The Federalists believed that it was important for as many states to ratify the Constitution as soon as possible. They were worried that a delay or a rejection of the Constitution would result in anarchy and civil strife. They attempted to convince people through their writings, which are now collectively known as The Federalist Papers.