You either have the votes or you do not. It is in an overall sense not clear to me what the strategy is other than delude oneself into thinking that media coverage is going to persuade enough Democrats to vote to bring the bill to the floor.
There is no way in hell that the media is going to embarrass any Democrats to do anything. And thus if you do not have the votes you do not have the votes.
Alas, the votes are definitely not there. This will hopefully keep Paxton in the Senate race. If it passes, Paxton will bow out.