The Constitution gives the American people a number of rights, but really does not explicitly give them any responsibilities.
The Constitution is mainly a document that lays out how the government will be set up and what it will not be able to do. The Constitution tells us what kind of government we will have. It then goes on to outline a number of things that government cannot do. The reason for this is that the people who wrote the Constitution were worried about the government having too much power. This is why they put all sorts of guarantees of rights into the Constitution and the Bill of Rights.
By contrast, they did not put in any responsibilities. In a sense, some responsibilities are implied. If we are to have a republican form of government, then we at least ought to take some responsibility for being politically informed and involved. But the Constitution does not actually tell us we must do these things. It does not tell us that we must vote. It does not require us to perform national service. It essentially tells government what not to do but it does not tell us what we must do.
Thus, the Constitution gives much more in the way of rights than it does responsibilities.