Hmmm...

I hesitate to go so far as to say we wouldn't have "won" the war... but we wouldn't have accomplished it in the manner and within the time frame that we did, I'm sure of that.

Without the TVA, Oak Ridge does nothing. In fact, I'd go so far as to say we don't have the bomb without the TVA, because Oak Ridge was sucking more electricity that all of New York City each and every day (1/5 of ALL electrical output in the country was being used by Oak Ridge to refine uranium). The University of Chicago's "Met Lab", where Fermi produced the first self-sustained chain reaction, was built with WPA funding in 1935-36.

By 1944, Wichita, KS was out-producing all of Germany in the field of aircraft manufacturing, due in large part to railroad infrastructure improvements made in the 30s. The same can be said of the "Arsenal of Democracy" that Detroit, MI had become. Railroads, freeways, and canals had allowed the influx of materials and the distribution of military hardware to flow out of the city at a rate never imagined prior to 1940. Textile centers like Scranton, PA were producing 10 million uniforms a month by 1943, and eastern PA and nearly all of West Virginia were pumping coal and oil out of the ground at rates previously unimagined... again, thanks in large part to the infrastructure that the New Deal had laid down.

Farm improvements that had begun under the AAA and other agricultural programs of the New Deal allowed American (and Canadian) farmers to meet and exceed all production demands made by the US military, and still provide a substantial segment of the civilian needs (supplemented with "Victory Gardens" and the like, of course). More importantly, the agricultural sector continued to produce such a volume of produce that it managed to almost single-handedly feed 85% of European needs AFTER the war was over.

The expansion of the electrical grid from less than 44% of the country to more than 75% of the country by 1939 must surely be seen as one of the greatest improvements to the infrastructure. Not because of the convenience of electric power to a home, but because of the increased productivity that comes with that advancement at every level of society. Farmers, factory workers, common laborers, everyone could spend less time working to live and more time being productive in an effort to win the war from the home front. Food canning operations, recycling centers, distribution hubs, small-scale manufacturing of items like ammunition, explosives, clothing, armour, machine parts, equipment and material production, and the exploitation of raw materials needed at every single level of our society could be found in every corner of the nation by war's end, thanks to the advancement of the electrical power lines across the country.