I stumbled across a short but fascinating work by the 19th-century philosopher Arthur Schopenhauer called variously the The Art of Controversy or The Art of Being Right. Wikisource has one version; another site has what seems to be the same English text alongside the original German. Read it in full!
His topic is controversial dialectic:
…the art of disputing, and of disputing in such a way as to hold one's own, whether one is in the right or the wrong—per fas et nefas. A man may be objectively in the right, and nevertheless in the eyes of bystanders, and sometimes in his own, he may come off worst.
The prefatory rationale for this discussion is interesting, but more useful are the thirty-eight tactics proposed in the body of the work. For example, here is #24 ("State a false syllogism"):
This trick consists in stating a false syllogism. Your opponent makes a proposition, and by false inference and distortion of his ideas you force from it other propositions which it does not contain and he does not in the least mean; nay, which are absurd or dangerous. It then looks as if his proposition gave rise to others which are inconsistent either with themselves or with some acknowledged truth, and so it appears to be indirectly refuted. This is the diversion, and it is another application of the fallacy non causae ut causae.
I have no idea of the popularity of this work among modern politicians, but even if they are entirely unaware, Schopenhauer literally wrote the book on argumentation—in 1831! The presentation is neutral, but I am inclined to read it as a spotter's guide to dishonest debate. Of statements by public figures and the online commentariat which infuriate me, not a single example falls outside his categories.
Armed with this knowledge, I have been able to point out the underlying fallacies or distractions when I see these methods in use, instead of falling prey to them. Often the author retreats from an unsupportable claim. When I prepare arguments myself, I check to see that I am giving my case honestly, and not using these shortcuts to merely appear persuasive via distraction.