First, let's start with a little civics lesson:
Amendment I
Congress shall make no law respecting an establishment of religion, or prohibiting the free exercise thereof; or abridging the freedom of speech, or of the press; or the right of the people peaceably to assemble, and to petition the government for a redress of grievances.
That's the First Amendment in it's entirety. I can't find a mention of FaceBook or twitter anywhere. No shirt, No Shoes, No Service. Same idea. It's a business and they can regulate your behavior if you want to be on their property.
They are all going to "self-police" like crazy in the future. Every democracy is finally going to realize the dangers they should have learned from the Arab Spring. Every government in the world is going to look at this situation and ask, if this can happen to the USA, why can't it be us? So every government in the world is now going to see social media companies as an existential threat.
As far as the US Congress is concerned, they were the targets, along with Pence. I think it's pretty likely that they understand that their own heads are on the line. Given some of the personalities involved I think that personal risk will motivate them more than simply the risk of downfall of the USA. So yes the social media companies should be running scared and trying to shape or avoid oversight, but it is probably too late to do much other than shape the future.
Proposals I have heard include:
-limiting the size of social media companies and encouraging competition
-any social media platform above a certain size would have greater oversight more similar to a television station
-require social media companies to exercise a greater degree of diligence with anything that is trending beyond a certain level