The U.S. Constitution doesn't directly say anything about overthrowing the government, aside from a specific, limited definition of Treason.
However, The Declaration of Independence of the United States says:
"We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness.
—That to secure these rights, Governments are instituted among Men, deriving their just powers from the consent of the governed,
—That whenever any Form of Government becomes destructive of these ends, it is the Right of the People to alter or to abolish it, and to institute new Government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their Safety and Happiness.
Therefore the Declaration of Independence says that we not only have the right but we also have the duty to alter or abolish any government that does not secure our unalienable rights, including life, liberty, and the pursuit of happiness.