Political leaders on both sides of the Atlantic failed to reach a compromise because it would have been very difficult for either side to back away from its demands. Leaders on both sides would have lost tremendous amounts of prestige for themselves and for the entities they represented.
If the British had backed down, they would have been weakening the image of their government. It would have looked as if the government would simply give in to any pressure from a group that did not want to obey the law. This is dangerous for any government. If the colonists would have backed down, they would have lost much of their ability to govern themselves. They would also have appeared weak and frightened in the face of danger.
For these reasons, neither side was eager to compromise.