It appears the route the Administration will take is removing CDA 230 protection status for Twitter. CDA 230 protects Twitter from being held legally responsible for hosting the comments of the users. Without the 230 shield, anyone could sue Twitter for a comment they didn't like. The cost of defending these lawsuits alone would bury Twitter in legal expenses.
IMO, such an executive order will be challenged in court, as there is no case law that supports the CDA 230 removal.