At present, the companies cannot be sued over what their users post online, or the decisions they make over what to leave up and take down.
Some politicians have raised concerns this "sweeping immunity" encourages bad behaviour.
But the chief executives say they need the law to be able to moderate content.
Facebook's Mark Zuckerberg, Twitter's Jack Dorsey and Google's Sundar Pichai were summoned before the Senate after both Democrats and Republicans agreed to call them in for questioning.
'A loophole'
