If you accept the premises, A's argument is sound; but I think most of us would sympathise with B and class it as fallacious, and ad hominem. This is because we do not accept the premise that all politicians are liars. There is a false premise that lies behind all ad hominem arguments: the notion that all people of type X make bad arguments. A has just made this premise explicit.
A: "All rodents are mammals, but a weasel isn't a rodent, so it can't be a mammal."
B: "That does not logically follow."
A: "*Sigh* Do I have to spell it out for you? All rodents are mammals, right, but a weasel isn't a rodent, so it can't be a mammal! What's so hard to understand???!?"
B: "I'm afraid you're mistaken. Look at it logically. If p implies q, then it does not follow that not-p implies not-q."
A: "I don't care about so-called logic and Ps and Qs and that stuff, I'm talking COMMON SENSE. A weasel ISN'T a mammal."
B: "Okay, this guy's an idiot. Ignore this one, folks."
A: "AD HOMINEM!!!! I WIN!!!!!"
Although the last line of B, taken out of context, might look ad hominem (and was seized upon as such by A), it should be clear that taken as a whole, B's argument is not ad hominem. B engaged thoroughly with A's argument. He is not countering A's argument by saying A is an idiot; on the contrary, having logically countered A's argument, and having seen A's reaction, he is arguing that A is an idiot.
