How efficient was the Nazi propaganda machine in sparking the war?

I did some research into how the German public was coaxed into supporting the war/ participating. I wondered how the 1939 invasion of Poland did not concern the people. This is an important topic because it shows just how effective Nazi propaganda was, and thus more readily explains how deportations to concentration camps only increased as the war went on and presumably more people were aware of the Holocaust. 

To begin with, the Nazis published an outcry against "polish atrocities" in reference to alleged violence committed against ethnic Germans in Poland.

Then, they staged an assault on a German radio outpost with SS soldiers dressed as Polish soldiers, and portrayed the invasion as self defense against polish "incursions".

They were careful to note that they were simply beating the Poles back and not engaging in war.

Once the war began the "final solution" was hidden from the public and never publicly detailed. Citizens were forbidden from reading allied papers condemning German atrocities and Goebbels reminded the population that these were all fake claims.

I believe that propaganda such as this, despite being incredibly efficient, still needed the compliance of the German public with Nazi movements. Basically I believe that even though many were deceived, a significant amount of the population had to still be ok with and know about the final solution and support the war. 

http://www.ushmm.org/wlc/en/article.php?ModuleId=10007822