You're absolutely right that in the ancient world they had political slander, but you're dead wrong in thinking that it resembles American politics in any way. In contemporary American politics the political actions and private lives of politicians are supposed to be (in theory at least) separate, to a degree. Hence what they used to say about senators arguing on the floor and then going out for a beer later on. Public affairs and private lives are supposed to be separate in American politics and it's not considered appropriate to begin bringing up your opponent's private life on the floor of the senate, or to use friends and relatives as political tools (again, this is a gross generalization, and much of what I'm saying here is vastly oversimplified to make a point).

It's not like that in antiquity, where your political life is very much inseparable from your social life. Politics, particularly in a place like Rome with a highly exclusive set of society holding great privilege (the nobiles), very much is your individual relations within society. Cicero gained his quaestorship by acting as a defense attorney for every important politician he could get his hands on, making friendships with them and gaining connections that owed him a debt of gratitude, a debt that was taken very seriously in Roman society. Pompey and Caesar forced through the Eastern Settlement and the Agrarian Laws by joining forces and using their combined political connections to pack elections and swing debates.

In such a social context it becomes very permissible to attack your opponent for peculiarities in his social life, irregularities in his family's status, perceived defects or deviancy in his character, and just general gossip. Roman society was also ruthlessly competitive for a variety of reason and any opportunity to get the leverage on your opponents was immediately taken by most people, at least those of any importance. Slander is dirty and very inappropriate by modern standards. Cicero accused Clodius of sleeping with his sister and for being a sexual deviant during the affair of the Bona Dea. He charged Piso with being an effeminate Philhellene and a degenerate, decadent Epicurean whose only desire was to satisfy his endless stomach--while he was simultaneously accusing him on the very legal and political charges of mismanaging his proconsulship in Macedonia. Cicero mercilessly prodded Antony, accusing him of everything from sexual perversion to alcoholism, and even his denunciation of Catiline was full of comments on Catiline's untrustworthy character and guilty spirit. Demosthenes said similar things in Athens a few centuries earlier, from whom Cicero clearly learned a lot of his material, accusing opponents of being descended from slaves and arsonists and so forth (my favorite is when he was debating with a guy in the Assembly, and his opponent's cloak slipped a bit, revealing a glimpse of his belly, whereupon Demosthenes immediately started ranting about how disgusting it was that he was so degenerate as to expose himself to the city). These accusations are often extremely specific and almost always untrue, or at least bending the truth. But they're very much a feature of Roman and Athenian oratory, in that you can use such things to trash your opponents, which is particularly useful when you know you don't have much on the guy but can use this stuff to make him seem so bad that he must be convicted. It's important to note that not everyone did this--dirty, low invective like this was a feature of certain styles of oratory and was never something that should take up the bulk of your speech. Caesar, for example, seems not to have used this style much (indeed, Caesar rarely used fancy rhetorical devices, though he was trained in them), preferring to state exactly what he thought quite directly and then use very plain and clear logic quite systematically to show why he was right and could not possibly be wrong--a technique that infuriated Cicero, since it was very good at stopping him dead in his tracks.