Congress does not have the votes to override Obama’s veto.
Ways to win here are by court injunction citing APA violations similar to the Executive Amnesty Injunction or bypassing FCC by going to offshore servers. Any attempt to shutdown incoming traffic could be met by court injunction on 1st Amendment grounds and by forming an effective underground.
The idea for the current injunction against Executive Amnesty originated from internet activity leading to a less than minute chance encounter with Texas AG now Governor Abbott. So the internet is powerful and is a force to be reckoned with.
On this issue they just might.