Proof by vigorous assertion (also known as hand-waving or arm-waving) is a rhetorical technique where an author attempts to bolster an argument by repeating himself or by reusing the same evidence stated in different ways.
To a sophisticated audience, proof by vigorous assertion is a dead giveaway that an argument is weak--most likely fatally weak. After all, if there were real evidence, you'd hear it.
To an unsophisticated audience, however, this rhetorical technique can add heft and bulk to an otherwise unconvincing argument. And it explains how great speakers can sell highly questionable arguments with hardly any evidence at all: all they have to do is restate themselves forcefully and in a range of different ways, and before you know it, naive listeners start agreeing.
All of this may explain why some politicians--at least those with a knack for turning a phrase--can convince the public to believe surprisingly illogical ideas.
The next time you listen to a political speech, look for reused reasons and evidence, especially in the form of soaring, memorable phrases. Instead of feeling inspired by the rhetoric, recognize that you're being fooled.