Unlike a natural right, government is conventional. It is created by people for a purpose. It rests for its legitimacy on their initial and continued agreement. One implication that Jefferson was eager to draw is that the people have the right to revoke their agreement in revolution. But the key implication is that government authority is limited.
People create governments to protect their natural rights.
That is, they agree to submit to a government, surrendering certain rights in particular rights to protect and enforce their rights themselves, to execute the law of nature, in Locke s phrase in exchange for the protection of the rest. The sole legitimate function of government, therefore, is the protection of rights. Protecting the right to pursue happiness entails more. How much more is a matter of debate. But the Founders intention seems to have been minimal.