As I thought, the key to this is trying to weaken the "common carrier" clause that protects social media sites from being liable for posts made by their users. (It almost certainly won't work, and if it does social media sites will simply move their corporate offices offshore rather than open themselves up to such liability.)
This because far-right trolls are mad that they get banned for being trolls -- now that a troll is President, they are demanding the right to scream at you without you being able to do anything about it.
Meanwhile Facebook, for its part, as many of my friends reading this can personally attest, religiously autobans people for, among other things, complaining about racism (largely driven by those same trolls filing spurious reports). This points to a key problem that people on both sides of the political aisle fail to realize - social media companies *can't* police speech because it costs too much money (and the outsourced labor they rely on often is unfamiliar with US cultural references needed to properly moderate content). The best they can do is automated systems that misfire all too regularly.
For its part, the White House yesterday led in the online harassment of a Twitter executive because his account had political posts that the White House didn't like. Kellyanne Conway read the man's Twitter handle on Fox during an interview and chortled about how "he's going to wake up to a lot of new followers now". Donald Trump Jr. (who is widely rumored to post on 4chan /pol) followed that up with his own repeated calls to action.
The theory and practice of Gamergate has arrived in the halls of government. And, true to Gamergate practice, they loudly scream that they are the ones being oppressed, while doing their best to destroy that which sustains them.