Impossible is a word people made up to describe their own failure. We held the might of [url=http://www.wikipedia.org/wiki/Godwin%27s_law]-godwinslaw!-[/url] Germany from these shore with little more than dark curtains and a few pilots mate. Anything is possible. Would you have said it was possible America to lose the war in Vietnam?
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Yes because the politicians were the ones attempting to wage that war. IE they did not let the generals actually decide much they instead debated in congress over what military targets to attack. While congress should be the ones to declare war they should not be the ones to wage and direct it........that's for the generals to do. That being said the germans did not outnumber you in the way that the American force outnumbers you. Plus the technology at the time was much less advanced. This made it more difficult for the Germans to wage the kind of war they wanted on Britain. Your infantry men...navy....pilots....they have all have to pull 20 -1 kill ratios 100% of the time if you were wanting to take on America's active military (this would be your entire military including reserves). Basically its an incredible long shot to say no doubt Britain would hold her ground through the entire war. Eventually you have to deal with the fact that you are vastly outnumbered. You cant say 1 country has more tech than the other......or more training than the other.......aircraft carriers have completely changed that way wars can be waged against island nations these days............basically it would take an act of God (or idiotic politicians) for America to lose. That being said...its still just a mental exercise as I cant imagine what would have to happen for these two countries to start fighting after being allies are such a long period of time. P.S. If you want to talk about tenacity what about a ragtag militia of men vastly out numbered, out gunned, and out trained taking on a military force and eventually forcing their surrender with some naval help from france (since there was basically no navy yet). :P