What effect did Hobbes have on the U.S. Constitution?

One effect Hobbes had on the framers of the United States Constitution was in his vision of political reality.
The framers were products of the Enlightenment. They were attracted to the theories of thinkers like Locke, who professed an optimism in the promises and possibilities of human beings.  Hobbes was decidedly more skeptical.  His political theories emphasized the need for a central authority to suppress the destructive instincts of human beings.  The framers wanted to avoid a monarch.  This was a political reality they had escaped under King George.  The colonists fought a revolution to be free of despotic rule.  Hobbes' theory reminded them of what they did not want in a new nation.  As a result, they pivoted towards a divided form of government, one that would prevent an abuse of central power.  
Another effect that Hobbes had on the framers was in his basic view of human beings.  The framers wanted to avoid Hobbes's state of nature.  Hobbes viewed human beings as “solitary, poor, nasty, brutish, and short.”  The framers sought to create a political world that could minimize, if not transform, these realities.  They believed that in giving individuals freedom to choose their destinies, human beings could be more than what Hobbes envisioned.  The framers believed that emphasizing positive freedom, where human beings could do great things, and negative freedom, where people could be left alone, would avoid a Hobbesian state of nature.  The framers embraced principles like republicanism and individual rights as ways to avert Hobbes' vision.  In these ways, Hobbes provided a reality the framers wanted to avoid in their new government.