I've got a few suggestions for you, but sadly, none are explicitly focused on rearmament. The GI Offensive in Europe: The Triumph of American Infantry Divisions, 1941-1945, by Peter Mansoor, is focused on the creation, training, deployment, and overseas service of the American infantry. Forging the Thunderbolt: History of the US Army's Armored Forces, 1917-1945 by M.H. Gillie and *Armored Thunderbolt: The U.S. Army Sherman in World War II * by Steven Zaloga are focused on the armored branch and its development in the interwar period and service in WWII. You might also have a look at the various entries in the official US Army history of WWII, available for free here: http://www.history.army.mil/html/bookshelves/collect/usaww2.html

Not "a book", but a series of books. You might find the series "The U.S. Army in WWII" Series , published by the US Army Center of Military History, useful. I think the series contains everything a general reader could use, and then some. See: http://www.history.army.mil/html/bookshelves/collect/usaww2.html