Should social media sites be held liable for the posts of extremists?

If the widow of a US government contractor killed in a 2015 Islamic State shooting in Amman, Jordan, wins her newly filed US Anti-Terrorism Act (ATA) suit against Twitter, there could be enormous consequences for social media sites.
Extremist groups are well known to use the internet to recruit members and plan attacks. Liability to victims of these attacks — and the treble damages available under the ATA — could mean significant exposure and reputational harm for sites frequented by extremists.