Which theory of the origin of the state most strongly influenced the formation of the government of the united states?

The theory is called social contract theory. Social contract theory, about as old as logic itself, is the view that people's good or potentially political commitments are reliant upon an agreement or assention among them to shape the general public in which they live.

The theory of a certain social contract holds that by staying in the domain controlled by some general public, which for the most part has an administration, individuals offer agree to join that society and be represented by its legislature assuming any. This assent is the thing that offers authenticity to such a legislature.