Nazi Germany got its way about Poland

Ah yes the Big One. Like the Anglo-American Nazi War, another fiction piece of bloodthirsty Ameriwank revenge porn where the self-righteous Yankees destroy Europe under the pretense of saving it from totalitarianism, and end up reaping a bigger body count and more devastation than Hitler or Stalin. I admit it might happen ITTL, but it would be a terribly dystopic outcome rather like the Cuban Missile Crisis going Hot, much more so than the British Empire being crushed and America going the Cold War way and waiting for Commie-Nazi Eurasia to reform or implode peacefully. ITTL the Axis coalition is going to include Germany, Russia, Italy, the Japanese Empire, Spain, Vichy France, and most of Eastern Europe as full members, pretty much everything from Lisbon to Tokyo would be an enemy power and a target for US nukes. Unlike OTL Axis, it would not be on its knees by land defeat and conventional bombing and waiting for the coup de grace, it would be intact and holding its ground, so it would likely take several dozen nukes across Eurasia in all Axis states to force it to surrender. Think of the huge body count and the utter economic, social, and environmental devastation, a whole half of the developed world sent to Mad Max land.

Thankfully, in all likelihood it won't come to that, for various reasons. First and most importantly, despite the Churchillian stereotype the Western Allies were not dictatorships and the Anglo-American people were not implacable robots under the unbreakable political spell of warmonger leaders. The Anglo-American electorate and vast majority of the ruling elites could have no idea nukes are coming in a few years nor how much effective they shall be. On its own, the British Empire is inevitably going to be overwhelmed and forced to surrender by the Axis coalition, if America joins the war it can certainly save Britain from surrender (but not from losing in the Med and the Middle East) and defeat Japan but it shall be utterly unable to defeat the Nazi-Soviet alliance in Europe. Any Anglo-American attempt to invade Europe, North Africa, or the Middle East would become a major, bloody fiasco much like Gallipoli, and the Anglo-American bombing offensive would not fare much better. An intact Nazi-Soviet Eurasia would certainly have the industrial resources to counter the Anglo-Americans tank for tank and airplane for airplane. Chances are the Anglo-Americans voters tire out of the seemingly futile bloodshed, kick out the warlike leaders from power, and impose a compromise peace that acknowledges the strategic stalemate as an inevitable fact, well before nukes become available.

Second, even if by some political miracle Western will to fight remains intact through a sustained, bloody stalemate, the Anglo-Americans shall be unable to achieve anything close to OTL air superiority over Eurasia, and this means their attempts to deliver WMD on Axis targets won't fare that well. Perhaps the Allies can penetrate Axis defenses enough to score a handful targets in Europe and Russia total, but this won't bring the Axis powers to their knees, and they are certainly going to be able to retaliate against Britain with chemical and radiological warheads carried by their own bombers and missiles. The British are going to develop second thoughts about letting themselves be destroyed so the Americans may conquer a devastated Eurasia. And in the time the Americans shall need to build intercontinental bombers, the Nazis and Soviets are going to develop nukes and intercontinental delivery means of their own. So in the end chances are once a few cities on both sides of the Atlantic are destroyed in a slow-motion limited WMD war, both sides are going to awake to MAD logic, realize mutual devastation is the worst outcome and serves no one's interest, accept a compromise peace, and settle down for a Cold War geopolitically not so different from 1984's world.