That was true in New England from early on, but not in the South, at least until much later.
And not in the West neither. It was a far far closer thing than school histories suggest. The Tories were numerous in New York and Philadelphia.
Well...since we have polls it has hard to tell exactly. There were areas in the South and the Middle states (Highlander Scots are a notable example) where Tory opinion was strong....but the whole south? I don't see the evidence. Good baromters of opinion in the South was not only the overwhelming support for the Patriot cause in Southern colonial legislatures but also the utter failure to recruit a "loyalist army" that could begin to match the patriots in numbers and zeal.