It is not entirely surprising to see the Iroquois Constitution having some relevance to the United States' vision.  Some of the initial framers of the American document of securing the nation were inspired by the Iroquois' attempts.  Franklin circulated Iroquois ideas to other framers as early as mid 1700s.  Delegate John Rutledge from South Carolina studied the Iroquois work intently and advocated that its introduction be a part of the American version:  "We, the people, to form a union, to establish peace, equity, and order..."  It is interesting to see the levels of similarities between both documents.  For example, Article 37 of the Iroquois Constitution states the following:

There shall be one war chief from each nation, and their duties shall be to carry messages for their chiefs, and to take up arms in case of emergency. They shall not participate in the proceedings of the Council of the League, but shall watch its progress and in case of an erroneous action by a chief, they shall receive the complaints of the people and convey the warnings of the women to him.

It is interesting to see the language about "complaints of the people."  This is representative of the popular sovereignty principle that asserts that people in the democratic nation can vote and have a voice.  Additionally, one sees a bit of "checks and balances" present in the language of "watch its progress and in case of an erroneous action by a chief."  The Iroquois might have influenced the idea of how government needs to be limited by other branches.  The framers did credit this idea to Montesquieu, but it is conceivable that they believed in this from the Iroquois, as well.  It should be noted that the language of the Iroquois Constitution heavily empowered women, something that the framers did not do and something that the U.S. Constitution did not do until the early 20th Century.