The main way in which the people of the English colonies developed these sorts of ideas was through the fact that they were English. By the time the American colonies were founded, England had been moving toward more democracy for almost four centuries. England was the most democratic country in the world. Over the course of the 17th century, England became even more democratic. By 1700, the Glorious Revolution had given rise to the English Bill of Rights. This meant that England already had a constitutional monarchy of sorts by 1700. The American colonists would have been very well aware of these moves and would have learned from them.
It is also important to note two other factors. First, many of the colonists had come to the Americas for what might be called political reasons. Notable among these were the Puritans, who came to New England to set up a society in which their religion could be dominant. This would have led the colonists to be more interested in self-government. Second, the English government practiced a policy of “salutary neglect” for many years. This meant that the government in England left the colonies more or less alone. Because of this, they came to think that they could and should govern themselves.