I think i disagree with the premise that Americans think that "'Poof' we created a resistance and won the war".
I can only speak of myself and the people I am exposed to, but our perception is that there were many failures in the beginning and that tenacity, adaptability and yes European assistance were responsible for the outcome.
My earliest exposure to the history of the revolution was probably the schoolhouse rock episodes on the subject. (On recollection it may have been the "Brady Bunch" episode on Benedict Arnold.)
School House rock episode (Shot heard round the world)
(every child my age probably saw this dozens of times during Saturday morning cartoons)
I know before I started elementary school I was exposed to the facts that
- The colonists lost the first few battles
- Initially they were extremely underprepared (Valley forge and so little ammo that "Don't shoot until you see the whites of their eyes")
- Things were going so badly at the beginning that one of our Generals defected (Benedict Arnold)
- The French and Spanish were of great assistance.
When I recall second grade (when we first covered American history) the facts that stick with me are balanced between hardships and failure, and tenacity and adaptability. On the one hand I remember vividly the descriptions of the blackened gangrenous limbs of Valley forge, but on the other hand the visions of men hiding behind rocks and shooting the British in formation was first proposed here.
As I progressed through my urban public school education I was exposed to the concepts that SSC mentioned in his post above except the one about DeGaulle. (Whom I still don't like or respect) I probably was exposed to a little more Revolutionary history than most as my highschool was named for a foreign general who assisted during the revolution (
Friedrich Wilhelm von Steuben)
As I said before I can only speak to my own circle of contacts, but I personally don't believe such perceptions are close to being universally held.