Actually I recall the Ken Burn's classic "Civil War" documentary specifically covers that...as only during the Civil War was usage of "These United States" changed to "The United States."
A lot of bad, and good, things can be dated to that conflict.
Actually, Ken was quoting Shelby Foote, a wonderful Civil War historian.
Shelby and Ken were both wrong, however.
Both terms were used since the Founding, sometimes in the same document.
“Are” was highly predominant initially, with “is” gradually gaining throughout the 19th century, by the end of which it was dominant.
The rate of increase in the use of “is” took a jump during our Civil War, but the biggest jump came during and after the War of 1812.