Which American family? My father was killed by a Japanese shell on the bridge of the cruiser San Francisco off Guadalcanal on November 13, 1942 so the effect on our family was very large. My mother and I and after a couple of months my new little sister had to move back from Hawaii to Massachusetts and live with my grandmother for the rest of the war, from November 1942 until the end in 1945.
The results were many, including my mother and I christening a ship, a destroyer escort, named after my father and the veteran's administration eventually paying my tuition at MIT from 1955 until 1959 when I graduated.
Meanwhile the country, which was pretty poor at the start of the war just coming out of the great depression, was booming with war work and then the work involved in putting Europe back together after the war and assuming a new position as unquestioned world leader. American science accelerated forward in leaps and bounds not only due to the advances made for military reasons during the war (nuclear energy, automatic control, electronics, computation) but due to the scientists that came to the United States from all over the world to be safe during and after the war. The GI bill paid for thousands of veterans and survivors such as I to go to college and the educational level of the population increased just in time to keep up with the scientific advances. Evolution of tension with Russia kept the pressure on to advance scientifically and militarily which kept technology marching ahead and employment high.
Damon is right to ask, "Which American family?" Undoubtedly each family was affected differently. He lost his dad very early on. I didn't, but my dad had experiences that were not nearly as bad as some, but worse than others. My mother and I went back to northern Nevada to live with her family until he returned (2.5 years later), and my baby brother was born there. He was with Patton's 3rd Army in France and Germany, and we were very fortunate that he came home physically unharmed. He, too, used the GI bill to further educate himself, but it took years before we lived on our own as a family. Until I was 13, we lived with one set of my grandparents or the other.
Every person who has any of this history in his or her family has a story. To generalize is to NOT recognize the individuality of it all.