The purpose of the words "hour" and "spring" is <em>to remind the readers that they must take action immediately to succeed against the British.</em>
These are Thomas Paine's words and they mean that he knows that the army is tired and that the men need rest but their safety depends on them. They have a lot to lose if they doubt so they have no time to think (hour) and time has come to drive off the invaders. They have to take action immediately (spring).