What shows that the US recognised the real threat to national security, is that they committed such priority to victory in the West, despite the obvious emotion to hit back at Japan.
FDR recognized that Germany was an existential threat to the US. He never saw this potential in Japan.
His policies and the records of his cabinet meetings show this. The formation of joint planning groups of the armed services (there was no Joint Chiefs of Staff at that time), and the planning requirements he laid out to them in 1940 and 1941, which drove America's armament-building and force expansion policies, were all driven by case scenarios of what it would mean to the US if the Germans beat the Soviets and/or the British.
I don't think there was ever a planning scenario for Japan conquering China or Australia. Incursions by the Japanese against US interests, sure, but no scenarios in which Japan actually became an existential threat.
The US would never have declared war because of, say, German aggression, because Germany had no means of carrying any aggression out.
Germany, in control of all of Europe, North Africa, and much of the Soviet Union, and perhaps the Middle East and India, would have been a threat to the continued existence (at least in it's historical form) of the USA. Roosevelt saw this as early as the mid- to late-1930s. By the time France fell he was no longer focused on arming allies to keep the US out of the war, but was actively trying to get the country ready for going to war -- he believed US involvement was coming and that he could not prevent it. But the political system of the US required the country to be behind him, and it was not, so he was limited in what he could do.
But he was looking, seeking, in full understanding that if he didn't figure out how to defeat Hitler, he might face a Hitler that he could not defeat.
Let us not forget that the atomic weapons project (later the Manhattan Project), the B-29 and B-32 were all initiated with the intention for use against Germany, and the B-36 project was initiated for use against Germany in the event of the loss of Great Britain to the Germans. All of this BEFORE Hitler declared war. These are clear evidence of just how clearly FDR perceived the threat.
So was Hitler wrong? Yes, in my book almost everything Hitler did was wrong. But that's a different question.
Was he mistaken in declaring war against the US? I think this is a very interesting what-if.
I think Hitler greatly underestimated the scope of American industrial might and the impact it could have on his war. He perceived that he was already fighting an "undeclared" naval war, at least. In this he was about 10% right, and about 90% wrong. Right in the technicalities of what constitutes acts of war, wrong in the scope as the KM was to learn.
50 old destroyers crossing the lines of neutrality vs. 500 new destroyers (and 1,000 smaller escorts and 50 escort carriers) actively at war made a BIG difference to the U-Boats.
Food, medicine, even guns and ammunition to the British crossed the lines of neutrality. A million-man army where even the infantry divisions that were more mechanized than German Panzer Divisions, on the European Continent, made a BIG difference to the Landsers.
I think Hitler greatly overestimated the impact of a U-Boat surge catching the US under-prepared along the Atlantic coast. It was effective. It was shockingly successful. It achieved far more than the KM had any right to expect. But again it was 10% vs. 90% … it was shockingly successful in how much tonnage of shipping was sent to the bottom for minimal losses in U-Boats. But it was completely irrelevant vs. the magnitude of the US military expansion (armaments and manpower, naval and army). He achieved all that he could have hoped for, and achieved nothing by it.
And I think Hitler greatly underestimated the limitations that the US Political system put on FDR. If he had not declared war on the US when he did, it would have been VERY difficult for FDR to declare war on German and Italy, and more importantly to establish a "Germany first" policy for pursuing the war. The American public was enraged against the Japanese, and would not have been nearly so accepting of defeats in the Pacific while forces when towards Europe if there was no war against Germany (yet).
I expect that one way or another FDR would eventually have gotten his war against Germany. But in the meantime momentum would already be established for the war against Japan. So I see Japan defeated sooner (perhaps by mid- to late-1944) before the US turns to Europe. Hitler is still in for a whooping, but what could he have done in the meantime?
I expect he would not have defeated the British. That was no longer in the cards by the end of 1941. Even in North Africa, Monty showed he could manage well enough if he got American supplies, and there's no reason to believe he wouldn't just because US fighting men were in the Pacific.
So also the Soviets showed they could fight the Germans to a stand-still with LL help (but no American feet on the ground in Europe).
So if the US doesn't finally get focused on building up forces in Europe until perhaps mid-1944, that means invading the continent in mid-1945. The Soviets probably don't get as far as fast as they did historically -- there's lots of good evidence that even by mid-1943 the Germans were pulling important units from the Eastern Front to face the Western Allies, and if no Americans in North Africa, then no massive German/Italian defeat in Tunisia, no Anglo/American invasion of Sicily, maybe no Italian withdrawal from the war in 1943.
But now the US forces land in 1945, about the same time the A-bombs start to become available. I don't see much happiness in that scenario for any side. For whatever we think of the body count of WW2, I think it goes up by a LARGE number in this scenario.
Hard to say much more -- too many variables. But I don't see anything looking better, only worse. So was it a mistake? Depends -- it probably hastened Hitler's demise, so we could say that was a mistake on his part. But I expect he would go down anyway, and not much more than half a year to a year later. Big diff? IDK. But he gets to take another several million innocents with him. Maybe that makes it a better choice for him, I can't say.
-Mark
(aka: Mk 1)