I'm sure they will try, but I don't think this is an issue that will change the minds of the senators currently holding out on filibuster/SCOTUS reformMy take.....
The Supremes will vote a majority supporting carry. This will set us up for the dems to cry foul and have a strong push to now pack the court. They will cry to the people about how their lives are in jeopardy now because Trump packed the court in his favor so now they need to protect us all by packing the court to give a more realistic and modern interpretation that reflects our society. They will argue that the 2nd was written for "then" and not now, thus their need to update courts to reflect today.
They will use fear and safety in order to get public support to pack it.