First, this thread will invoke the name of The Unmentionable Sea Mammal.
Second, I'm assuming a POD well before 1939, enough that conditions change to make the successful invasion of Britain possible. I don't want to get bogged down in the details, but assume that by 1942, Hitler controls Britain. Ireland is neutral in Germany's favor. Pearl Harbor happens as OTL, and Hitler makes the boneheaded decision to declare war on the US.
My question is, would it be possible for the United States and Canada to launch a transatlantic invasion of Europe?
Obviously, this would be a colossal undertaking, making Operation Overlord look like child's play. But if anyone had the raw industrial might to do it, it would be the United States.
With that in mind, I'd like to propose a few approaches:
Operation Overlord
An attack on France as in OTL. I'm not even going to go into detail over how stupid this plan would be without a secure nearby base. Even if they could land and keep the KM off their backs, the Germans would simply ship in troops by land.
Operation Saratoga
A US/Canadian invasion of Britain (with more than a few Free British troops thrown in). Why is this a better idea than Overlord? Simple: it offers the opportunity to cut off German reinforcements by blockading the Channel. A highly complex operation in its own right, I'll grant you, but we're probably talking about shoving what is undoubtedly a much larger Atlantic Fleet between Britain and the Continent. Under this circumstance, the answer to the question of building carriers or battleships would be to build as much of each as both sides wanted.
Operation Morrigan
A massive US/Canadian fleet heads into the Atlantic and lands in... Ireland! Turns out that the Irish have been in secret negotiations with the US, possibly including allowing them to retain Ulster if they help, and threatening to give the whole island back to Britain and enforce Prohibition if they don't. The aid Ireland would need to hold off the Germans arrives. The Allies use Ireland as a base to liberate Britain and eventually the continent.
Operation The World Is Round In Case You Forgot
As an alternative to invading over the Atlantic, the US and USSR establish a joint command. US forces cross Siberia to join the Red Army on the Eastern Front. Politically a mess, but the thought of the combined manpower and industrial capacity of the United States of America and the Soviet Union on the same front is, frankly, terrifying.
Operation Pale Horse
I fear the ultimate answer to my question is a rather radioactive yes. If it came down to it, the US could simply nuke its way into Europe. But I'd rather this not happen.
Also, if this is a completely ludicrous idea, feel free to say so.