A little later in the speech, he offered an answer:
If we get economic calamity even worse than we have now, you will lose your rights. And we have to be vigilant and watch.
What happened in Germany, when the Weimar Republic printed up so much money and you carry it around in wheelbarrows? There was a collapse, and they actually voted in a Hitler. You could get something like that in our country if we're not careful and vigilant.
Watch (the key excerpt is around the 5:25 mark):
It's perhaps not the key point, but Paul mangles German history here. In fact, the hyper-inflation of the years after the First World War had largely stabilized by November 1923, when Hitler, lacking popular support, tried unsuccessfully to seize power in the Munich Beer Hall Putsch. It wasn't until the Depression of the early 1930s, triggered by the 1929 Wall St. crash, that the Nazis began to receive significant popular support, leading to Hitler becoming chancellor in 1933.
Leaving that aside, Paul's belief that an economic collapse could lead to Americans voting in "a Hitler" seems worthy of attention.