After Reconstruction, the country was "put back together" very slowly and gradually. The North and South grew to be more like one another only very slowly. This process has still not been completed, and it was still very incomplete as recently as the 1960s.
The country grew back together as events happened that gave the people of the North and the South more in common. These were events like WWII, which affected the whole country in more or less the same way and led to the people of the two sections feeling as if they had more in common than not.
Perhaps the greatest thing that has caused the country to get almost completely "put back together" is the movement of people. The South has become economically stronger (to some extent) than the North and many people have moved from the North to the South (and vice versa). This has led to so much mixing that the two sections are no longer nearly as distinct as they once were.
Technically, the country was back together once Reconstruction ended. In more of attitudinal terms, however, the country was put together only gradually as attitudes changed.