@Putin: It's a good thing that Americans take some steps to recognize how the government has historically and I guess contemporarily been so awful to Native Americans, but that's not a good way to do it. And I don't find a politically-motivated effort (that's the push that ended up being the congressional statement, I think) from 1987 terribly impressive.
I suppose we could play the historiography game, but I don't really want to. I will say that Jack Rakove, to my knowledge the top historian today on the making of the Constitution, is strongly against the Iroquois influence theory.
There was some doubtlessly considerable indirect influence in terms of promoting the notion of a confederation of different people, but even more so in terms of seeing Indians as a threat which demanded a stronger government. I haven't seen an argument yet which I find convincing to prove that the Iroquois Confederacy actually influenced, in any direct way, the creation of the Constitution. There are two main reasons:
a. the main thinker behind the Constitution was James Madison, aka "Father of the Constitution," who was (like most of the rest of the Convention) strongly influenced by his deep immersion in the European intellectual traditions of governance and by his experiences in practical politics. These are provable, stated influences which don't need any additional examples or inputs.
b. More generally: The Americans were busy killing or expelling Indians as fast as they could. Part of the background of the Revolution is the desire to free American settlers from English limitations on taking land from Indians in the Ohio Valley etc. Indians were not considered equal to whites or able to live in American society, even after various tribes take gigantic efforts to Americanize themselves (e.g. the Cherokee). Why would Americans take influence from a people who they clearly saw as inferior?
@fulhamish That makes sense, at least the origins of where you heard the tale, but I don't think there's much evidence for it.