I think there are a number of assumptions underpinning your question regarding a certain similarity between the attitudes of modern America to its serial killers and 1946 Germany to the Nuremberg defendants that need to be assessed. I think the best way to break down the differences that exist is through a side by side comparison.

In America, the act of serial killing represents, to some extent, the apex of (for lack of a better word) "anti-social behavior". What I mean is, the crime of murder has been among the most serious of crimes in Western society since the establishment of laws. Furthermore, among murders, there is a clear sliding scale from (on the "most acceptable" side) crimes of passion, where some event caused the murderer to temporarily lose control and act on their emotions, to (on the "most unacceptable" side) calculated motiveless murder on the other, where the killer has no connection to or personal motive for killing the victim, and furthermore acts with forethought and premeditation. This kind of murder is near-universally regarded as one of the highest possible tresspasses against the values of modern America, it is likely that nobody who reads this will have ever encountered a person who believes that serial murder is acceptable. Such a belief would be regarded as madness. This has been true for as long as the phenomenon of serial murder has existed.

The relationship of Germany to the Nuremberg defendants was massively different. One year previous, nearly all of the people who were being tried in Nuremberg occupied high positions in government, the military, private industry, or the press (the only exceptions being Rudolf Hess, who was already imprisoned after his disastrous solo flight to England; Franz Von Papen, who had smartly been avoiding the spotlight as the war drew to its conclusion, and didn't seem to do all that much after returning from his post as Turkish Ambassador in 1944; and Hjalmar Schacht, who by that point was a prisoner in either the Dachau concentration camp or else the Alpine Fortress in Tyrol, depending on the exact date, and who, not coincidentally, was one of the three acquittals at Nuremberg). While 1945 was a hard year for everyone involved (and I will discuss this further in a bit), if we look even further back, say 5-10 years, we can see all of the defendants not only in positions of power, but also in a position culturally that is literally the opposite of what I described with the serial killers above. The Nazi Propaganda machine, in co-ordination with the Gestapo, were quite effective at taking the wheel of public opinion and during the years of Nazi success (say 1935-1941) before the war started going sour, they were able to control public opinion with ease, which of course meant that anyone affiliated with the upper echelons of power was regarded with the highest praise.

Now, at this point we need to make a distinction between what the public were supposed to think and what they actually did think. This is a controversial issue, and one that has a number of respected proponents taking very different sides. But, I think most scholars would agree that prior to the war going sour, the vast majority of the public ran the spectrum from active support to quiet toleration of their Nazi rulers. While I hate to make any kind of blanket statement, a couple of examples may at least give you an idea for how the public saw the future Nuremberg defendants:

Hitler was liquidating the past, with all its frustrations and disappointments. Step by step, and rapidly (as we shall see in detail later), he was freeing Germany from the shackles of Versailles, confounding the victorious Allies and making Germany militarily strong again. This was what most Germans wanted and they were willing to make the sacrifices which the Leader demanded of them to get it: the loss of personal freedom, a Spartan diet (“Guns before Butter”) and hard work. By the autumn of 1936 the problem of unemployment had been largely licked, almost everyone had a job again and one heard workers who had been deprived of their trade-union rights joking, over their full dinner pails, that at least under Hitler there was no more freedom to starve.

Shirer, The Rise and Fall of the Third Reich

The vast majority of political jokes during Hitler’s reign were basically uncritical of the system, playing on the human weaknesses of Nazi leaders rather than on the crimes they were committing. Imperial Marshal Hermann Göring, for instance, was a popular target because of his pompous appearance and his love of glamour and medals. One typical joke ran: Göring recently added an arrow to the many medals on his chest. It’s there as a directional sign: “To be continued on my back.” Like many Göring jokes, the tone here is familial and affectionate, rather than harsh. The political humor of the time never alluded to the fact that Göring was a sadist who became a mass murderer as well. On the contrary, the imperial marshal appears most often as a sort of pompous but ultimately likeable Falstaff. In fact, Göring’s all too apparent human weaknesses endeared the second most powerful man in the Third Reich to broad segments of the population. The fact that he was a cold-blooded, cynical despot with no regard for human dignity did not prevent Germans from sympathizing with him right up to his postwar suicide while in Allied captivity.

Rudolph Herzog, "Dead Funny: Telling Jokes in Hitler's Germany". And a couple more Goering jokes from the same book for good measure:

Two pictures, one of Hitler and one of Göring, are hanging on the wall of a school with a space left in the middle. A teacher asks, “What should we use to fill the gap?” A pupil stands up and says, “A picture of Jesus. The Bible says he was nailed up between two criminals.

The Nazis’ rule is over, the verdicts have been spoken, and Hitler, Göring, and Goebbels are hanging from the gallows. Göring turns to Goebbels one last time and croaks: “I told you everything would be decided in the air.”

All this goes to indicate that while the relationship between the German citizens and Nazi elites was complex, it was vastly different from America's relationship with serial killers. However, as the final joke indicates, towards the end of the war, when things were going badly, things started to change. While the Gestapo tightened its grip over the everyday words and actions of the people, they were not able to keep a certain cynicism from appearing. However, even in these circumstances, the relationship does not match up with how America views serial killers. By the time of Nuremberg, most German citizens were happy that the war was over, disillusioned by the horrors they had endured, and ready to move on from the disastrous past four years. However, that does not mean that the people who had ruled them up until very recently suddenly underwent a complete 180 in everyone's minds. You can look at the numerous actions taken by the allies (including Nuremberg itself) to override more than a decade of propaganda as evidence of this. There were still many people loyal to the old regime, though every day they were fewer and fewer in number.

With all that being said, we can now begin to look at your actual question. Unlike American serial killers, where less than one in 100,000 supports their actions, and those who do are acting in some kind of perverse rebellion against societal values, there was a significant number of people in Germany who still supported the Nazi higher-ups. Again, Goering is the easiest one to look at since, after Hitler, he was the most prominent member of the Nazi party and had been so since before they took power. As the jokes I quoted indicate, public opinion of Goering in the early years ran from wholehearted admiration to lighthearted humor about his ego and weight. By the end of the war, people were blaming him for the massive aerial bombardments that had destroyed much of Germany, and the things being said behind closed doors took on a darker tone. However, there were still many people who could not let go of the previous idealized image they had been presented, and this is evidenced by the fact that right before his execution (and long after copious evidence for his role in the crimes of Nazi Germany had come to light) he was able to acquire access to a cyanide capsule so as to avoid his execution by hanging.

So, the best way to answer your question is to say that, in 1946, the defendants of the Nuremberg trial were still far too close to their previous positions in power to be regarded anywhere close to the way we regard our serial killers, and because of this, unlike the very small minority of American's who admire mass murderers, their was a sizable percentage of the German population who still held the Nuremberg defendants in high regard.