This will not be your top answer, at least I hope it isn't, but there is no obvious consensus among historians on this issue. Those in the Native American camp will cherry pick references to the Iroquois League/Confederacy (eagles, arrows, Articles of Confederation, etc.), while other scholars are quite Eurocentric, claiming that no evidence exists that Native American societies influenced the foundation of U.S. government. Good luck on this, I'm looking forward to the answer, as well.
I can argue for the counter point. The US constitution borrows more from the Roman constitution and Greek political thought. The idea the Greeks had was that there are three forms of government: monarchy (rule by 1), oligarchy (rule by few), and democracy (rule by all). The Romans made arguably the first mixed constitution which combined elements of all three, having a Senate, Consuls, and popular assemblies. Indeed, the US constitution is remarkably similar to the Roman constitution, except where the Roman constitution evolved over time, the US's was created at once, so its cleaner. The US constitution is based off of these principals, distribution of power, and a system of checks and balances.
First we have the executive branch (rule by 1, monarchy), who carries out the law.
Then congress (democracy, representative in this case), who makes the laws.
Finally the supreme court (oligarchy, serve for life after appointment), who interprets the law.
I hope my comment's not too late, but I did a mini-paper on this topic a few years back. There are arguments to be made for both sides.
Ben Franklin was knowledgeable about Native American affairs. As a printer, he published transcripts of Native American treaty council proceedings and those pamphlets sold well, both in America and in Europe. When Franklin proposed the Albany Plan in 1754, he cited the Iroquois Confederacy as a successful example of such an union. Although the Albany Plan failed, it can be seen as the forerunner to the Articles of Confederation.
Other than Franklin, however, it's not known how interested the other founders were in Native American governing styles. In the notes James Madison took on the debates at the Constitutional Convention, he makes no mention of the Iroquois, but other European confederations, however, were cited by those present.
Just want to chime in on the point about the Iroquois Confederacy inspiring American political organisation. A good article looking at the ongoing debate among historians and tribal knowledge keepers on this issue, and its broader real-world effects, is Gail Landsman, "Informant as Critic: Conducting Research on a Dispute between Iroquoianist Scholars and Traditional Iroquois," in Indians and Anthropologists: Vine Deloria, Jr., and the Critique of Anthropology, Thomas Biolsi and Larry J. Zimmerman, eds. (Tucson: University of Arizona Press, 1997), 160-176.
Edit: formatting.