I'm thinking about it now and frankly find it hard to believe that the US would have had a difficult defensive war vs Germany. Germany had a very difficult time invading England and this shortcoming would have only been magnified if they tried to cross the Atlantic.
Another example I can think of is the very reason the US felt it needed to save Britain in order to push the Western front. Germany would have had no safe staging area for which it would be able to invade from outside of Cuba, which is pretty far inland and could have been attacked from the North, West, and South, making it a terrible defensive location. If Germany tried for the Northern cape of Canada, the invasion would have still been difficult if the Canadians/US prolonged the war into the Winter, as proven by Germany's huge losses pushing into Russia and Stalingrad.
Thoughts?
This would depend on what you mean as "a threat" do you mean "could they launch any attack" or "could they successfully invade" or "could they have eventually become a threat"?
Someone better acquainted will undoubtedly come along soon, but I'd point out that Nazi Germany didn't/couldn't invade Britain and that was in range of airstrikes from mainland Europe to soften them up and across the relatively narrow English Channel.
Compared to sending troops across the Atlantic, though, invading Britain would have been logistically a walk in the park. WW2 Germany wasn't a true naval power either, and it was fighting the two greatest in the world. It'd seem almost insane to suggest they could have supply lines across the Atlantic and defend them under those circumstances.
There's also the question of manpower. So are we assuming some peace with Russia scenario? Because given the substantial losses in Russia and entanglements on the Eastern Front it'd seem that the Nazis wouldn't have the manpower they'd need to invade another country, let alone one on the other side of the world.
All in all I'd be extremely dubious about their ability -at any point- to project power across the ocean. Unless you're assuming some sort of alternate history? But I'm happy to add more and with more details once I know the parameters of the question.