Good thing the overwhelming majority of the world's industry is located in the one country who's developed their entire arms industry to defeat the Americans.

And Nazi Germany didn't have submarines loaded with nukes lurking who knows where. The US has such bloodlust that people here will bay and screech for the nukes to be used as soon as there's even the slightest bit of humbling felt.

Mobilizing of the rest of the world's industry helped accelerate the end of the war, but I wouldn't say "required." Nazi Germany would have eventually lost against the UK, CCCP, or USA and tried to fight all three at once. Any of those could have defeated the Axis Powers on their own. It would have just taken a lot longer, possibly decades. The genocides would have higher death tolls than they did.

As far as actually requiring as many members of the Allies? Doubtful. The US and CCCP production outputs were both greater than the rest of the Axis combined. Britain's industry was more than Germany and Japan, but less than both together. It was, however, on the world's largest aircraft carrier.

Regardless, the Axis invaded too many countries, spreading them too thin. Even if the US and UK decide to stay neutral, the Soviets are still being assisted by China, Poland, etc. for troops and logistics while their factories sit well-protected east of Moscow. And eventually, the fascists would run out of stuff to steal, which is what allowed them to start the war to begin with. By 1945, they were running on fumes. Even in this alternate timeline, the Germans are still going to have problems with fuel and food. Maybe they make it to 1947 before they feel the strain. They still didn't make it more than a year into Barbarossa before running into the kinds of problems from our history.

As pointed out below, I'd be more concerned about rogue American elements using nukes from submarines or other clandestine shit like "briefcase nukes." I don't think the US has the industrial capacity to wage war like the Germans did because the US can't even keep up with the wars it fights against smaller countries like Afghanistan or Vietnam. A peer war with China or Russia or both is the end of the US. I'm not even sure it could do anything significant in a nuclear exchange. China may already have the tech to shoot every missile out of the sky while landing all of theirs.

I would be worried about a sub firing a nuke at Saigon or Hong Kong out of pure spite as the rest of America burns.