I don't think news of the holocaust leaking out would dent Nazi Germany. Nazi propaganda was incredibly insidious and powerful. There was more than just top-down megaphone work; Goebbels had the ability to construct a reality out of thin air.
First off the incredible power of dramatic propaganda (not something anybody can really escape these days, but at least there's a plurality of viewpoints today and people are instinctively sceptical because if you believed everything you saw on TV you'd have everything but your organs harvested by lunchtime). If I give you a political book, you're going to read it but the idea that it might be propaganda will never be far away.
OTOH, if I show you a propaganda movie, or worse again a long succession of them, it remains powerful even if you're suspicious of it. This is because you're viewing the action rather than judging a text. The events occur right in front of your eyes so that even if you're suspicious it still bypasses the logical mind and goes straight into the subconscious.
In addition to cinema and TV they also had (for example)...
The ability to turn people into marionettes. E.g. a Hiter Youth group are instructed to give reports on a propaganda broadcast. Each must address the group and parrot the party line. Because the participants cannot communicate safely with each other, they're each left with the impression that all the others believe the message wholeheartedly.
The astroturf manoeuvre. Goebbels was a past master at this. Nazi party functionaries would be given anecdotes and jokes to relate loudly in Cafés, bars and other public places. The propaganda message was often covert and subtle.
The phony debate. Orchestrate superficially vigorous debate on some topic but with one team deliberately pulling its punches.
The theatrical event. E.g. The Kristallnacht. Having organised the pogrom himself, Hitler stepped in after a few days in the guise of a restraining personality. This combines the astroturf and phony debates into national-scale political theatre.
Add in lavish state resources devoted to 'positive' propaganda lionizing the Nazi edifice into that brew and you have a mix it would be barely possible to resist unless you had extensive prior exposure to free media.
Even if the Holocaust had been carried out to a conclusion, the Jewish spectre would remain part of Nazi propaganda simply because it was a key crutch of the regime psychologically. They literally couldn't do without the Jewish bugbear.