That particular argument pretty much has to start with the opening of this seminal essay:
In a recent bulletin of the Superintendent of the Census for 1890 appear these significant words: "Up to and including 1880 the country had a frontier of settlement, but at present the unsettled area has been so broken into by isolated bodies of settlement that there can hardly be said to be a frontier line. In the discussion of its extent, its westward movement, etc., it can not, therefore, any longer have a place in the census reports." This brief official statement marks the closing of a great historic movement. Up to our own day American history has been in a large degree the history of the colonization of the Great West. The existence of an area of free land, its continuous recession, and the advance of American settlement westward, explain American development."The Significance of the Frontier in American History"
Frederick J. Turner. 1893
I don't want to get too caught up in the rightness of Turner's thesis; what's important here is its resonance. People responded to the idea that the frontier was the defining influence on the country. It struck them as sensible and profound and it was something they wanted to talk about.
From Wikipedia:
Turner's emphasis on the importance of the frontier in shaping American character influenced the interpretation found in thousands of scholarly histories. By the time Turner died in 1932, 60% of the leading history departments in the U.S. were teaching courses in frontier history along Turnerian lines.
One frontier that had obsessed and arguably defined the nation closed just as another frontier that would do exactly the same thing was opening. I'd argue that this deepened the mystique of technology, but that's a point for a future post.