stillwaters somewhat vaguely talked about the Night of the Long Knives, where the SA was purged. That was probably crucial to getting the German Army's approval and support as that left-wing part of the NSDAP were pretty rampant in the "vaccuum" years of the collapse of the Grand Coalition sometime in 1930 until Hitler's ascension into power in 1933. [Btw as a sidenote I don't think they were called the Wehrmacht until 36-37, there were still the Reichwehr. Though for the source of uniformity just call them the German Army/Armed Forces]
Hitler's "Volksgemeinschaft" really restored pre-1918 German societal values, and this meant prestige to the army. Remember that the Reichswehr remained pretty much a conservative force in the Weimar due to that pact.. Eber-Groener iirc. In my German national study essays I made much of the "right" and "left" leanings of the different power groups in Germany.
And to avoid generalizing, the Reichswehr/Wehrmacht were not exactly fully behind Hitler - yes the army was headed by conservative right wingers, but they were not necessarily Nazis - it was not until Hitler did some purging of his generals around 1936, such was fabricating rumours about a general's homosexuality [sorry I don't know the general's name this is off the top of my head] that he really "Nazified" the army.