As part of the enabling acts to make the territories states they were required to sell some of their land to pay for the roads.
So it was the states it went through paying for it- not the feds.
President Madison vetoed an internal improvement bill that was heavily weighted in favor of Virginia in the hopes of getting his signature (it's funding of a Virginia canal to the Ohio river would have tied the west to Virginia instead of through the Erie Canal to New York and prevented the Civil War IMHO- but, alas, that is neither here nor there).
Well, it was far more than a "national road." The project as drawn up by Gallatin was $10 m., more than the entire Fed. budget at the time, and much of it was canals, not roads, to be built at federal expense. See my book, "The Entrepreneurial Adventure: A History of Business in the United States."