We have to be careful here because we simply don't have the evidence to start talking about "most". There were no opinion polls conducted in the Third Reich asking "How do you feel about the Fuhrer's death?" or "How would you gauge your loyalty to the Fuhrer?". Instead, what we must rely upon is interviews after the fact and primary documents such as letters during the war in an attempt to construct an approximation of such a statement like "Most Germans felt. X".

That said, based on such evidence, we can make some educated guesses. Let's break the groups into three camps: average civilians, military leadership, and rank and file Nazi Party members.

First, the civilians. The average German wasn't a Nazi Party member, and they weren't enthused by the prospect of another war. What was paramount in their minds was the First World War, and avoiding a prolonged conflict was very important. The quick victories over Poland, and then France, brought a lot of enthusiasm for both Hitler and Germany's prospects, and in the fall of 1940 there was a general expectation that Britain would seek peace. As the war dragged on into 1941, people started to feel resentful towards Britain more than Hitler. Starting the war with Russia brought a great deal of anxiety, and as the war dragged on in the ensuing years, enthusiasm for Hitler waned, even as victories continued to roll in. I think the breaking point though was the defeat at Stalingrad. The regime tried to hide it for as long as they could, but several hundred thousand men disappearing off the face of the planet can only be hidden so long before their families notice the lack of letters. However, outright resistance against the regime was not particularly active, even as the war dragged on and defeat became certain. There simply was no organizational structure left for dissidents to coalesce around given the harsh treatment any active dissenters received prior to the war even starting, let alone when it was actively going on. Even before their suppression, civil society in Germany had never been particularly strong at standing up to the existing power structures that the Nazi Party had used to get into power.

Second, we have the military, or perhaps more accurately, the officers. The officer core of the military was still dominated by the old guard Prussian elite at the start of the war, the same men who had been running the military since before there was a Germany. They were part of the key faction that brought Hitler to power. Even the junior officers were largely of this faction at the start of the war. However, as the war dragged on more and more officers were being replaced, both low and high, with Nazi men. The junior officer core in particular started to become dominated by real Nazi Party members (as opposed to the paper holding officers who joined as a requirement), first as the military expanded and then as losses were replaced. Senior officers were slowly relieved for perceived failures as the war in Russia wore on. Stalingrad was also a turning point for this section. Hitler had by this time been seen as being far too meddling (an accurate description) in military planning, and this debacle was sort of the straw that broke the camel's back for the old guard in the military. A myth arose that "If only that Austrian corporal would let us run the war it would have been won" that even some Western historians have bought into. However, as an aside, those same experienced officers also had their fair share of failure, so that is pretty much as accurate a myth as the 'stabbed in the back' myth was. Hitler can be blamed for starting the war, but the German Army still played a role in losing it. At any rate, the military faction started turning against him after Stalingrad. As I said, the civilian population was not likely to be able to form a capable resistance to Hitler, but the military could. However, as mentioned, over the previous years the old guard that had placed him into power, and likely represented the old force strong enough to take him out of power, had been diluted. So they schemed on how to replace him and stay in power themselves, and failed on both accounts.

Finally, we have the rank and file Nazi Party members, the true believers. This subset of Third Reich society was obviously the last to lose faith in him, and, besides those who continued to believe in him until the end, most lost faith once the Red Army was crossing the border and certainly by the time the Rape of Berlin was in full swing. We can see a general progression in thought; 1939 - Woo, we are seizing our destiny! 1940 - We knew the Fuhrer was right! 1941 - He was right before, so we have complete faith! Dirty commie Slavs! 1942 - It will all be fine! 1943 - The battle must be complete, we must commit fully! 1944 - We can still win except for the Jews and dissenters at home! (this one never made sense to me) 1945 - Fuck Hitler. He bamboozled us! The writings of the time lack a distinct sense of self-reflection and responsibility on the part of the Nazi Part members, which sort of makes sense I suppose. Hitler was cheered when he was winning, gained some cred among these people looking for answers and faith, and then completely blamed for the devastation wrought upon them (much as the officers blamed him, rather than themselves).

Source: Richard J. Evan's The Third Reich Triology