There was a particular instance where Thomas Jefferson called John Adams a hermaphrodite (via a supporter with a newspaper) [0]. Adams apparently responded by spreading a rumor that Jefferson was dead. I believe that technique was learned from Benjamin Franklin, who "predicted" the death of a rival almanac publisher. [1]

There's much more in the way of antics among the founders of the US, but this isn't unique to them. Classical antiquity even has stories of some of the childish stuff that politicians got up to.

EDIT to add example: IIRC Cicero accused Clodius of incest and a number of other things [2]. Clodius responded by accusing Cicero of acting as a tyrannical king while he was consul. Some of the insults don't hit the same today, but this is supposed to be seriously petty stuff.

The Cicero example wasn't anonymous, of course, but then again anonymity in classical antiquity would have been a good way to make sure your story didn't survive to the modern day. Having said that, there are stories about some of the stuff that was written in graffiti in Rome.

I'm not sure if I'd call any of this stuff "worse" or not, though there was more political violence in the ancient world. I guess it depends on what you include under the term "discourse".

For what it's worth, the origins of our word "invective" apparently come from Latin [3][4]. Apropos if true.

[0] - https://www.merriam-webster.com/words-at-play/are-presidenti...

[1] - https://en.wikipedia.org/wiki/Titan_Leeds?wprov=sfla1

[2] - https://en.wikipedia.org/wiki/Publius_Clodius_Pulcher#Sex_an...

[3] - https://en.wiktionary.org/wiki/invective

[4] - https://en.wikipedia.org/wiki/Invective