They could still blame the problems on a) imaginary Jews, b) Jews living in other countries, c) other "inferior" humans, d) Germans influenced by Jewish thinking, e) non-Jewish traitors of the new Reich.
(If socialist countries can be used as an analogy, they never had a problem to find some enemy to blame, regardless of how many of those alleged enemies they already killed decades ago.)
My take on some historical religious/social/political movements:
The best strategy for complex social movements is not honest rationality, because rational, practical approaches don't generate enthusiasm. A radical social movement needs one charismatic radical who enunciates appealing, impractical ideas, and another figure who can appropriate all of the energy and devotion generated by the first figure's idealism, yet not be held to their impractical ideals. It's a two-step process that is almost necessary, to protect the pretty ideals that generate popular enthusiasm from the grit and grease of institution and government. Someone needs to do a bait-and-switch. Either the original vision must be appropriated and bent to a different purpose by someone practical, or the original visionary must be dishonest or self-deceiving.
There are exceptions to this pattern that, I think, prove the rule when you look at them more closely:
And then there are just exceptions:
One interesting aspect of the pattern is its hysteresis. Once idealism has been successfully co-opted, the resulting organization can continue to siphon that credibility indefinitely, while dismissing its more radical demands.