Political philosophy begins with the question: what ought to be a person's relationship to society? The subject seeks the application of ethical concepts to the social sphere and thus deals with the variety of forms of government and social existence that people could live in -- and in so doing, it also provides a standard by which to analyze and judge existing institutions and relationships.
Political Philosopy details with "why" a governing system "should" do what it does to effect and the relationship between an individuals, groups, and "society". Therefore, these discussions focus less on specific methods of governance and more on the rationale and justification for the governance system.
One of the phases that has always stuck with me from my college Philosophy course is "ought implies can". That is if we say a moral agent "ought" to do something, then we imply that the moral agent has the power and capability to do it. If the moral agent doesn't have the power or capacity to accomplish the action then saying they "ought" to do it is an exercise in futility. This statement, so simple, yet so profound is from Immanual Kant a key Enlightenment Philosopher.
Kant also articulated another key tenet to which any government respecting liberty should adhere. His Categorical Imperative is expressed in three ways, but perhaps the easiest formulation is "people are ends in and of themselves and are not means to an end. In other words governments should not use people to accomplish governmental ends/objectives. Rather, as Jefferson said in the Declaration, power flows from the people to the government and governments exist to secure liberty and its blessings for the people. This is direct juxtaposition to a government that convenes a war for its own purposes and forces people to pay for it through taxes and compulsory service in the military.
The rebellion in the American colonies stemmed from almost those exact conditions. While many Americans have heard the cry "No taxation without representation", the specific conditions came from Great Britain's experience and costs of the French and Indian War, also known as the Seven Years War. The British king, whose family came from Hannover, Germany and still maintained its possessions in Hannover, spent a great deal of money to defend Hannover during the war as well as to fight the French in the American colonies. After the war, the British government had both a huge debt to pay and a large army they could not readily disband without creating social upheaval in England. The solution was to tax the colonies as to send the Army to the colonies to "protect" them and have the colonists pay for the Army there. The colonists were told to pay the burden for services they had not specifically requested, could not turn down, and in the case of Hannover, did not benefit from. The colonists were treated as a means to an end.
Kant was not the only Enlightenment Philosopher that shaped American political philosophy. There were several others, to include Voltaire, Lock, Hume, Montesqueu, Diderot, Mill, Benthan, and Fichte among others.
But the roots of American political philosophy go even deeper, back to Plato, Socrates, Epicurus, Zeno, Aurelias, Seneca, Cato, Cicero, and others. Most of the founders had a "classical education", which meant they learned and studied Greek and Latin. As part of these studies, they read many of these philosophers and statesman.
Another key influence was the Iroquois Federation. The Iroquois's federal government was a key model for the founders and influenced their thoughts. While we might not consider Iroquois great philosophers, that may well be largely due to our small knowledge and understanding of Iroquois history and culture. Samuel Grey, in his paper In the Form of a Longhouse: Haudenosaunee Political Philosophy and Social Contract Theory, starts hthe paper with an interesting quote:
"Thy message is good," said the woman; but a word is nothing until it is given form and set to work in the world. What form shall this message take when it comes to dwell among men?"
"It will take the form of a longhouse," replied Deganzawidah, "in which there are many fires, one for each famil, yet all live as one household [...]"
- The White Roots of Peace