Although Locke and Rousseau wrote prominent treatises on the social contract, Thomas Hobbes introduced the idea of it. He argued that human beings were evil in nature, and thus needed to enter a contract in which everyone basically agreed not to kill each other (i.e. in his natural state, although completely free, man would always be wary of subjected to another man's brutishness. Whereas in society we are all supposedly better off-even if there are sacrifices involved-because there is an agreement binding each man into behavior that's meant to contain man's evil nature).
The national government got stronger thanks to the Articles of Confederation being replaced with the US Constitution. The Articles of Confederation was America's first constitution. This constitution lasted roughly a decade, as it was extremely ineffective and gave the federal government very little power. For example, the federal government could not collect taxes or force states to follow national laws.
When the US Constitution was passed, the federal government gained significant power. This included the creation of an executive branch, the idea that federal laws trump state laws, and the ability to raise funds in order to create a national military.