Verified answer

Traditionally, members of the House of Commons were elected. According to Jefferson's political ideas, it was this that gave Parliament legitimacy--they had the consent of the governed and were elected by it. Because Americans could not vote in the elections, Parliament had no legitimacy in the Colonies, according to his view. What's more, acts of Parliament often tried to block acts of the local colonial councils and assemblies, where the colonists *did* have a say.

By contrast, the kingship of Britain was hereditary and god-given. The people of Britain had never had a say in who was king of Britain, so there was nothing odd about the colonists not having a say in it, either--this didn't go against tradition. So long as the King did not hold too much power, but shared it with democratic institutions (like Parliament), there was nothing wrong with the idea of being loyal subjects of the King.

Initially, many revolutionaries didn't want independence from Britain at all. They didn't mind being subjects of the British crown, but they resisted the acts of Parliament, which they viewed as illegitimate, and wanted the acts of their own assemblies to be recognized. It was King George III's support of Parliament, and his rejection of any diplomacy the colonists attempted, that would make the idea of total independence popular. Had King George been more diplomatic, the colonies might have simply gotten a more autonomous status within the British Empire.