1. Why wouldn't Germany's skies be defended by the Luftwaffe if they had won the ground war. Where else would the planes be?
2. Support for the Nazis would certainly grow if they had actually won the land war, the morale of the population would be very high in this case.
3. A single large nuclear attack, unless it could cripple the enemy's ability to wage war, would serve little purpose against a population whose morale is high from victory other than to make them angry and even more willing to fight.
Consider yourself a German, your fatherland just defeated every other nation in Europe. Now, the only enemies that resist you are on the other side of the sea, and they just brutally murdered a million of your countrymen. Are you going to immediately surrender or wish to see those that bombed you wiped from the earth?
It is only the sustained bombing, which would be nearly impossible to properly execute, that would eventually break the population's spirit.
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Had Germany achieved air superiority over the Channel, they could very well have crossed it. What would happen once they land is another matter, but competently done an invasion of Britain could succeed. An invasion of America would be possible through a number of routes, but it would be extremely risky.
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