This phrase is referring to two things.  It refers to King George III of England and it refers to the pharaoh in the Bible who refused to let the people of Israel leave slavery in Egypt.

In the Bible, Moses tells the pharaoh that God wants him to free the Israelites.  The pharaoh initially agrees but then changes his mind.  The Bible says that “the heart of Pharaoh was hardened” just as Paine refers to the “hardened … Pharaoh of England.  By alluding to the Bible, Paine is saying that King George III of England was acting like the Egyptian pharaoh.  He was being obstinate and “hardened” and would therefore not let the Americans go free just as pharaoh would not let the Israelites go free.