Trump's (empty) threat would actually make sites like Twitter more restrictive, not less - 2020-05-28
Trump is cooking up a legally dubious executive order which will probably direct the formation of a panel to investigate political bias by social media companies and make recommendations to change existing law.
It seems unlikely anything will come of it and I'll try to explain why I think that.
The Washington Post article suggests that Article 230 (of the Communications Decency Act) is on the table. Section 230 is basically a safe harbor for online service providers so that they're not liable for their users' defamatory or harmful content. Without it, online service providers would be forced to police their users' content because they'd effectively share their users' liability.