The era which most deeply influenced the writing of the Declaration of Independence was the Modern Era and the illuminism movement. The Declaration of Independence was written in 1776, when illumimism movement was at its peak, and its influenced was heavy on the declaration as it emphatiziced the natural rights of the people, for example.
The Nazis built on this. Most crucially, I think, was the Enabling Act of March 23, 1933. And this is when the Reichstag amended the Weimar Constitution— they required a 2/3 votes to do so— and gave Hitler emergency powers for four years.