Our deepest fear is not that we are inadequate. Our deepest fear is that we are powerful beyond measure.
Second, this suggests that simply by landing a single US unit in Casablanca, (which happened in 1943, historically?)...
8 November 1942.
...My understanding was that Vichy stayed neutral (officially) until at least after D-Day?
Immediately after the Torch landings the Axis implemented Operation Anton in order to occupy the island of Corsica and all of Southern (Vichy) France. This took less than a week, after which all remaining Vichy forces were disbanded. The Vichy government more or less continued to exist in metropolitan France until after D-Day, but governed at the behest of German wishes.