It was not an overnight thing, and Hitler essentially couped them first.
Hitler's rise to power coincided with a simultaneous rise of Communism and Nazism in Germany. The conservatives in question (e.g. Hindenburg and the Catholic Center Party) favored Hitler over the Communists. After the Reichstag fire they gave him the power to crack down on Communists with paramilitary operations. All through this time Hitler consolidated his power with the German government, making sure that important posts were filled with people who were loyal to him.
The deciding moment, if there was one deciding moment, was the passage of the Enabling Act. The NSDAP used all of their power to sway the Reichstag vote, including actually physically prohibiting opposition from showing up. They received assistance from the Center party only after giving their leaders assurances that President Hindenburg would retain a veto, but after the passage of the Enabling Act the state was essentially a dictatorship.
Who would have led such a coup against Hitler at this point? The Communists and Social Democrats? Already unpopular and now banned or oppressed by the brownshirts (the Sturmabteilung). The moderate left? Not strong enough. The conservative center? By this point, not strong enough. The military? They more or less supported Hitler because he wanted to make them bigger and stronger. (And eventually non-supporters were purged.)
There are two wrong popular American perceptions of Hitler's rise to power. One is that it was a totally populist movement, a genuine will of the people. The other is that Hitler just showed up and took control and forced everyone to do what he said. The truth is somewhere in between — a mixture of just enough popular support (and popular dislike/distrust/fear of the Communists, who were for a time waging an active, violent insurrection to gain control of various areas of the country) to get into a powerful position, mixed with enough means and moxie to leverage that position into a dictatorship that, once embarked upon, could not be reversed.
When I was an undergrad and studying this stuff more closely, the book I found most useful for fully understanding how the Nazis really took over and consolidated their position in the German state was Turner's Hitler's Thirty Days to Power: January 1933. It sounds like a weird self-help book, but it does a great job of emphasizing how many people underestimated Hitler, and how their support of him was more about their lack of support for what they saw as the alternative (Communism).
Interestingly, army generals planned a coup several times. However, it wasn't because they disliked nazism, but rather because they feared to lose the war. For example, some generals were sure that a war with Czechoslovakia will be a disaster, as the country was supported by France and England. However, when Hitler fooled England and France into actively helping him to partition Czechoslovakia, and he got this land without a single shot - the reason for the coup was gone. So those generals did nothing.