Regarding longevity of the Nazi regime there are a few questions I would like to add for consideration, and apologies if I'm repeating what others have said or asked.
A) how does the German population react to Hitler leading successful consecutive conquests of Poland, Denmark, Norway, Netherlands, Luxembourg, Belgium, France and the Soviet Union, presumably before the end of 1942?
B) in such a scenario, how long would Britain and the USA deny themselves trading with much of German dominated Europe? (Assuming peace with Britain is achieved prior.)
C) if this is, relatively speaking, a quick War and the Soviet Union up to the Urals is conquered by the end of '42 what are realistic German casualties rates?
D) how quick can the oil flow from the Baku oil fields (and perhaps Iran too), and how does this effect both military and peacetime domestic industry?
E) as mentioned previously by others, feeding people is a large issue - and only semi jokingly I ask, how quickly can the now surplus Panzer I, II and III tanks be converted to tractors? Will Nazi feudal romanticism give way to industrialised farming techniques?
A) with great joy and a sense of national pride that would make an American crowd chanting U.S.A. at an Olympic sporting event appear to be subversives looking to overthrow the government. There would also likely be massive number of previous doubters who now bought into the idea of a "destined People". It would actually be remarkably hard to prevent this sort of mindset, even if the government wasn't built on German racial superiority as a given fact.
B) If the British have already surrendered there would be trade fairly quickly. Depending on when the British capitulated (yes, capitulated, there was no "reasonable peace" with the Reich, you won or you were conquered and occupied sooner or later, see: Czechoslovakia) the U.S. may never have engaged the Reich at all.
C) Impossible to be certain. It very much depends on when/where the Soviets collapse (which, BTW, is fairly hard to bring about). If the initial shock manages to get Stalin liquidated, or, alternately, if Stalin wipes out his best commanders in the early weeks of the war, the numbers are vastly different than if the collapse happens in late 1942-early 1943, allowing the WAllies to trap a major German ground force in North Africa & the Western Desert and having another full campaign year of the Eastern Front meat grinder.
D) Again, depends on when the Soviet collapse happens. If it is early on, then the oil fields may be surrendered mostly intact, if it is after a hard fight in the South, it would be at least a year, maybe more. The time depends of if the British are already completely vanquished or are still able to resist. With out access to British and U.S. equipment the Reich will have something of struggle in getting thoroughly destroyed production infrastructure back on line.
E) Less trouble than you might imagine. The Reich planned to reduce the population in General Government, Poland, Ukraine and European Russia far more quickly than they expected to refill it with German settlers. In some documents it is stated that the goal is to move 10 million settlers into Poland/General Government over a decade. Since those areas will have had 30+ million people "removed", with the survivors working at starvation rations, including those working on farms, you would have the entire Steppe's output available to feed what would eventually be roughly 60+ million fewer people (as Extermination through Labor combined with those transported virtual certain death in Western Siberia). Food, well at least for German citizens than those personnel selected for "Germanization", would not be a serious issue.