I can't imagine what the political landscape looked like during the first post-war years
Nazi crimes that were hugely used as propaganda by the allies helped. So did the feeling of national shame of losing another war.
It is hard to quantify how quickly nazi sympathies "died out". It is a fact however that nazi prestige suffered immediately and greatly after the war was over. Looking at the 1949 Elections in West Germany might guide us a bit:
29% Social Democrats. The SPD was famous before the war for resisting the nazis all the way through. They were the only party to as a whole oppose the Ermächtigungsgesetz of 1933. Well, we should assume the communists would have done too, but they were all arrested or in exile by then.
25% Christian Democrats. The Christian Democrats are centrist moderate right-wing moderately religious. Possibly a few disguised nazis voted for them, as their predecessor, the Central Party, even collaborated with the nazis to some extent in 1933. Franz von Papen, Hitler's vice chancellor of 1933, had been part of the Central Party until 1930, before becoming independent.
11% Free Democrats. Think, to an extent, British LibDems. Both Social Liberals and National Liberals united under a party. Maybe a few nazis in there.
5.8% Christian Socials. Basically the Christian Democrats of Bavaria. So we should maybe count 30% Christian Democrats.
5.7% Communists. No Nazis to be found here, I assume.
4.2% Bavarian Party. Conservative Localists. Note that the NSDAP of the nazis originally came from Bavaria and had one of its stronger showings there.
4% German Party. This is the first really hardcore right-wing party we can find here. They were in favor of veteran care and otherwise pursued anti-communist agendas.
1% German Right Wing Party. They were the poorly disguised neo nazis.
So, judging from four years after the end of the war, democracy had become popular in the west once more. (Inofficial) Neo Nazi organisations up until the recent NPD would consistently score between 2 and 5% of the electorate and, since reunification, have found a new power base in the former East Germany.
I would however like to show you a few more examples. There was one party that literally tried to be the NSDAP #2. This was the Sozialistische Reichspartei, the Socialist Party of the Reich, SRP.
The SRP, and this is true, demanded 'loyalty to the reich', they wanted to protect the 'honor of the German soldier' (whatever that means), and they demanded a "solution of the jewish question". They did not critisize the Holocaust for the idea, however they were not okay with the methods undertaken.
They had split from the Right Wing party in October of 1949 and had also been supported by former SS commanders like Leo von Jena. Von Jena had been a backup representative of the NSDAP in the thirties and had been the city garrison commander of the SS in Berlin in the early fourties. He, according to his personal files managed by the SS, left the position, conincedentally shortly before Operation Valkyrie and the Stauffenberg Plot, because of his poor health.
The SRP openly glorified national socialism, and was banned by the West German constitutional courts in 1952. One of only two parties, the other one being the German Communists in 1956.
Also, several notable Nazis and Wehrmacht Commanders were openly in favour of Nazi propaganda and supported either the German Party or the SRP. One of them was Heinz Guderian, the legendary doctrinal father of the Blitzkrieg Strategy. He was part of the "Bruderschaft" (brotherhood) of former nazi commanders, as according to the British Secret Service. This Bruderschaft was led by Karl Kaufmann, former provincial governor of Hamburg and vital supporter of the early holocaust deportations.
So, to sum it up: The population quickly kissed the nazis goodbye, but the nazis themselves, at least in part, had their habits die hard. To be fair, people like Erich von Manstein would later on go on to help the young Federal Republic. Others like Dönitz just took their punishment and then made sure to never become the subject of public attention again.
As always, a clear answer is not easy. I hope however my presented evidence helps you.
Sources:
Bodenstein, Lars Ole: Die Rolle von Karl Dönitz im Zweiten Weltkrieg. Die kritisch historische Analyse eines Mythos, 2002 (Language: German)
Federal Republic of Germany: Official Federal German sources regarding the Election Results of 1949 until 2013.
Guderian, Heinz: Erinnerungen eines Soldaten, 1951 (Autobiography, Language: German)
Piekalkiewicz, Janusz: Der Zweite Weltkrieg, 1985 (Language: German)
Wucher, Albert: Marksteine der deutschen Zeitgeschichte, 1991 (Language: German)
(Note: I am horribly sorry that most of my sources are in German. I tend to study my fatherland in my own language.)