When arguing with somebody, there’s nothing more frustrating than pure dismissal of your strongest argument with a wave of the hand. Pence codified it with “There you go again with that Mexican thing.” It’s a combination of 3 fallacies (from wikipedia):
Appeal to the stone (argumentum ad lapidem) – dismissing a claim as absurd without demonstrating proof for its absurdity.
Argument from (personal) incredulity (divine fallacy, appeal to common sense) – I cannot imagine how this could be true, therefore it must be false.
Onus probandi – from Latin "onus probandi incumbit ei qui dicit, non ei qui negat" the burden of proof is on the person who makes the claim, not on the person who denies (or questions the claim). It is a particular case of the argumentum ad ignorantiam fallacy, here the burden is shifted on the person defending against the assertion.
It also uses the technique of thought-terminating cliché – “a commonly used phrase, sometimes passing as folk wisdom, used to quell cognitive dissonance, conceal lack of thought-entertainment, move on to other topics etc. but in any case, end the debate with a cliché—not a point.”
Trump will probably do the same in the next debate, seeing that it worked so well for his running mate. The question is, is he going to do it as effectively, without bombast?