Was there as much support as it's purported to have had?
There was remarkable and widespread resistance to Hitler and the Nazi party. The Social Democratic Party (SPD) organized anti-Nazi demonstrations when Hitler gained power, and in March 1933, all Reichstag members of the SPD voted to oppose the Enabling Act which gave Hitler unlimited constitutional authority. They then established a sophisticated underground organization to oppose the Nazis which consisted of “exiled leadership, newspapers and party activists.” Their resistance persisted until they were finally shut down by the Gestapo between 1935 and 1938. The SPD’s efforts continued after that, but with less success and visibility than before.
Around the same time, communists in Germany, specifically the KPD (Kommunistische Partei Deutschlands) resisted the Nazi regime as well. “From 1933 to 1939, 150,000 Communists were detained in Nazi concentration camps and a further 30,000 were executed.” The KPD was the first political organization to have the wrath of the new regime thrown upon it, after which it was forced to go underground and become a clandestine resistance group.
In addition to major political parties showing opposition, many industrial workers went on strike to oppose the new regime. These included workers in armament factories deliberately working slowly, to strikes by workers building the autobahn, to some organized opposition from factory workers in cities like Hamburg. These kind of activities became more prevalent as the war dragged on and the Nazis were forced to use labor from foreign workers.
McDonough, F. (2007). Opposition and resistance in Nazi Germany. Cambridge: Cambridge University Press.
Purported?
Well, there was a huge movement and tension against Hitler, the NSDAP in general. Many intellectuals spoke out against Hitler. The Konzentrationslager were used for political prisoners in the beginning. Journalists, priests (who spoke out against Hitler), communists, leaders of countermovements were the first prisoners in the KZs. (Mainly, Konzentrationslager in the west were used for this purpose.)
In the beginning of the 1930's, political murders and street fights happened daily. Beside the fact that political opponents became prisoners, the NSDAP used military forces to end the street fights and the chaos in the cities. It's one of the reasons many Germans kept silent during the dictatorship or supported Hitler (because they wanted the street fights to end).
Furthermore, there was a significant group of people in high positions, who refused to raise the flag of the Third Reich in university, Handelskammer and so on. They just lost their jobs.