The central achievement of the American Revolution was to demote government to a role of cop on the beat. The monarch stopped being the sovereign; the citizen became sovereign instead. Self-government became an aspiration for all people not just rulers.
The idea became prominent, at least for a while, that government's proper role is to secure the natural rights of the citizenry. There was nothing there about a nanny or a regulatory state. John Locke, who identified the most principled version of the classical liberal conception of government, argued that since in "the state of nature" – i.e., prior to civilized society – some people may pose a serious threat to others, a system of laws is needed so as to mark everyone's sphere of authority, a region within which one is in full charge and which others must respect instead of trespass upon.
One's life is the beginning of this sphere; one's liberty follows as does one's private property. What a government is needed for is to keep these safe, to secure the rights to life, liberty, property and whatever derives from these. That is the point of government, nothing else. It is a vital function since without it criminal conduct would very likely go unchecked. But like referees at a sports event, government isn't meant to get involved in the game, only to make sure it goes on peacefully, with everyone's sovereignty secured.
This view of government was, of course, radical to the core. Instead of the century's old top-down rule, by some king or tsar or gang, everyone is supposed to rule oneself and his or her dominion. All interactions among people would in time be voluntary and peaceful. And from this arrangement would emerge a productive, creative, free community and not a hive or colony as with bees or termites.
That is what is individualist about the American system, namely, that a country is to serve the objectives of a great variety of unique citizens and that one particular way of living was not to be imposed on all by a ruler. Government is to serve the citizenry, not the other way around. And contrary to some thinking on the topic, we are not all in it together as in North Korea and other collectivist political communities. Instead of being a sphere for just one kind of life dictated to by a ruler, America was to be a sphere for an immense variety of different lives coexisting peacefully, competing and cooperating, not marching to the same tune.
The details of the American idea course would, of course, be complicated and diverse but one idea was at the center of it all: None may violate the basic principles on which such a system rests, the basic rights of every individual. The only role for force was to be defensive and retaliatory. No one may initiate it with impunity, not even for noble goals a leader might wish to force upon the rest.
That is the American political alternative, the American political tradition, not the collectivist ideal pursued by some political thinkers and "leaders."