What it says on the tin.
During the war, there were constant rumors that the Reich had begun construction of a final redoubt in the Alps, where they and the remnants of the Wehrmacht would hold out against the combined allied forces.
Ultimately, this all turned out to be a complete fabrication designed as a smokescreen to distract the Allies, and Hitler never approved the plan. However, what would it take to get the Alpine redoubt actually constructed? How would it affect the Allies strategy?
The biggest obstacle to even getting off the ground would be Hitler. Creating a Redoubt in South of Germany to fight a last ditch battle would mean accepting the possibility of a defeat on all fronts. It would be a tough sell and I doubt many would even try to sell it to him. Given the logistics involved the building and staffing of such a thing would have to start late '43 or early '44 at the latest and Hitler would not have been sold on the need for it, thinking a great victory is just around the corner due to the hand of Providence being upon his shoulder. And without Hitler's consent, few would dare to spend resources to build a project of such scope. All it would take is for a shit weasel such as Chief of Staff of the Nazi Party Chancellery Martin Bormann to start a carefully crafted "casual" conversation with Hitler about such-and-such defeatist taking resources away from the German Army fighting for its life and the valiant Fatherland to build a place to hide and it would result in a mouth frothing speech from Hitler, hard stop and mass arrests. If Hitler could not be won over then someone would have to sell the idea to Bormann. This would involve a, uh, brave or at least a reckless individual, because you would be essentially telling a shit weasel a secret which he could then use to hang you at any moment. Not that Bormann would endorse such a plan anyway, for plausible deniability reasons in case it was discovered he would want to be able to tell Hitler he had nothing to do with it. But still, you need Bormann. That leaves out Goering. Not that I'd trust post-Stalingrad Goering to do anything of the scope involved, but the Fat Man still had industry contacts and would at least grasp the scale of the project (or have some bright boys in his Air Force explain to him, while chowing down on pills, swilling wine and playing with a tiger cub, while possibly dressed as a Viking). Bormann loathed Goering in '45 and I doubt they were on b-day gift terms in late '43 either. Besides there is no way you can trust Goering to keep his trap shut about a project of just magnitude and he'd be terrified of being found out by Hitler and probably betray his co-conspirators. Speer would probably be able to build it from a tech perspective, but he had no access to manpower and there is no way he would put his technocratic neck on the line in a pact with a shit weasel. That leaves us with Himmler and the SS. Himmler would be looking over his shoulder during the whole of the exercise, but he could do it and had the resources available, provided he had a cut out man to deal with Bormann. In my opinion, he would most likely use Gestapo Chief Heinrich Müller. I think Müller and Bormann could come to an accommodation and Bormann could see the need for a redoubt.
The actual building of the Redoubt would be a massive undertaking, requiring manpower to both build and staff, as well as transportation. The financial costs of building it would be a non-issue given the funds available to SS, SD and the Nazi Party. There were already projects involving the creation of monster guns (vulnerable as they were to air attacks) and vengeance weapons (rockets and the thankfully never developed A-bomb). Conventional weapons for the personnel to be stationed would be available as well, as the guns were available and if anything the transportation of it from German war factories to Southern Germany would probably cause less delays than sending weapons to the front. Transportation of building materials would be problematic. Heavy Allied bombing would make itself known and disrupt any plans. The use of slave labor and indentured foreign workers was already being fine tuned for other projects, but this would be something else. The sheer scope and Germany's deteriorating position would probably see the project being drastically revised as more and more roadblocks appear. There could still be a redoubt, but nothing so massive and grandiose as Himmler's crabbed fantasist mind envisioned. I picture the whey faced bastard sitting in his chair, his black tunic open to better rub his belly through his white undershirt as psychosomatic stomach pains shoot through his body while he stares at the reports and revised blueprints on the table, blinking and trying to come to terms with the fact the giant ballroom in the shape of three interlocking swastikas with twelve 20 foot tall marble statues of big breasted Viking maidens guarding the perimeter will just not be feasible.
The end result would be a redoubt capable of supporting several thousands of troops and their support staff. How many thousands is hard to say. I doubt it would be anything approaching the numbers being bandied about in Allied reports. There would also be a problem of staffing. Himmler had control over the so-called Black SS: the administrators, book burners, torturers, temple destroyers, bed sheet sniffers and desk bound killers. His control over the Grey SS - the Armed Forces doing actual fighting against the Allies - was far from absolute. There was no oath of obedience to Himmler. The oath was to Hitler. Himmler could find the SS troops to staff the redoubt and even fund and provide the support they'd need to present a military challenge to the Allies, so long as Hitler lives. Once Berlin falls and Hitler kills himself... all bets are off. Himmler would be asking SS to fight a cause whose Leader had fallen. There could be appeals to continue on as Christians had without Christ (a million apologies for making this comparison, but I am doing it to illustrate a point), but a Nazi Germany without Hitler is hard to picture, because all power in the Nazi Party derived from Hitler. Himmler was given power because of how close he was to Hitler not because of official titles (most of which he appropriated or invented or modified). Same for Bormann. Same for all Nazi officials. I mentioned this in another thread, the main ideology of Nazi Germany wasn't fascism it was Hitlerism. He who is closest to Hitler wields the most power. Without Hitler, there would be a power vacuum too large for someone such as Himmler to fill, redoubt or no redoubt. I do not think SS would fight on in a redoubt after Hitler dies in Berlin. Nor do I see the German military fighting on without Hitler, for there would be really no point. They were ready to surrender to the Western Allies by the end of it, though they did fight for Hitler's Germany more ferociously and with greater dedication than they did for Kaiser's Germany, but that's a different topic for a different day. If Hitler stays in Berlin, then it all goes as it went on, Redoubt or not. Ironically, I do not see the Allied strategy changing much from our timeline to this one either, as the whole broad front offensive as envisioned by Gen. Eisenhower was done precisely because of the fears of the Redoubt.
A question worth exploring is would have Hitler contemplated going to the Redoubt if it was presented to him shortly before the ring shut around Berlin and prevented any flights. There would have been an opportunity in April 26, 1945 when a plane was landed in Berlin by Hanna Reitsch, the talented female pilot whose recklessness, blonde hair, blue eyes and utter lack of political education made her a beloved mascot of both Goering and Hitler (he personally awarded her an Iron Cross First Class, which must have been quite moving for all involved). Ms. Reitsch was quite able and willing to get Hitler out of Berlin. As a matter of fact, when she did leave Berlin, Russian troops assumed it was Hitler escaping and shot at it, but did not bring it down. If in late April 1945, Hitler was presented with the Redoubt as a fait accompli, his reaction would have been unpredictable. The other question would have been, who would have the guts to tell him?
There was no question of Himmler or Goering (by this point the old boy would have figured it out, but be utterly unsure of what to do with the information) putting the question to Hitler. Neither the shit weasel Bormann nor Gestapo Müller would put their head on the block for it either. Ms. Reistch would have been reckless enough to do it, but she would not be trusted to try to present an argument. I think out of all the terrible creatures around Hitler in that Bunker the only one for the job who could and would want to reach Hitler on a personal level was his hapless friend Walther Hewel. Ostensibly a diplomat, Hewel was a long term confidante and was generally called upon to run the day to day business of Hitler's staff. Cornered by powerful men and explained the facts of life, I can see Hewel being the dummy sent to explain to Hitler that the Redoubt was not as he was previously told a nonsense piece of propaganda to confuse the enemy but actually exists and had been build out and now awaits Hitler's august presence. There would be babbling, hand shaking rage of course and threats of hangings and shootings, but once it subsided and Hewel pressed his case with the skill of a head waiter explaining why the tainted cow meat might be a bad idea and why the rabbit is fresher and better, I think it might have swayed the shattered psyche of Hitler. It would certainly appeal to his warped reality, a chance to lead a Germany from ashes to glory from the heart of "his" Germany - Bavaria, not the awkward Berlin. Ms. Reitsch's plane had room for two. She could transport Hitler to The Redoubt. Berlin would collapse within a day as news would undoubtedly leak and I dot think many of the people in The Bunker would survive, though I see Himmler, Goering, Bormann and Müller getting out. Now it would not just be the question of SS troops, but regular German military carrying out the orders of their Leader as well. The Western Allied response would not change as much as slightly pivot. But I am not sure about the Russians.
It is hard for me to picture the Bolshevik intelligence services not sniffing out the Redoubt and its capabilities ahead of the Western Allies. Given the threat Hitler presented and the skin crawling fear Stalin felt of Western Allies making a deal with Hitler, it is more than likely than the Russian forces would pivot South as well and it could very well be a race, officially cloaked as a Soviet-Allied encirclement of the hated foe. Whoever reaches the Redoubt first would suffer terrible casualties to break through to forestall their allies getting to Hitler first. I do not think it would be possible, and the attack on the Redoubt would ultimately be a Soviet-Allied combined effort, awkward as such an effort would have been. I am not sure how long a Redoubt would prolong the war if Hitler occupies it, but in the end it would have been overwhelmed as readily as The Bunker. The worst case scenario would involve an atomic bomb being dropped on the German resistance in the Redoubt by the United States, with thousands upon thousands of lives being lost as a result.