unconstitutional then - it would get struck down.
Unconstitutional? No question.
Will it be struck down? That is a big question.
Traditionally the SCOTUS views the issue of internal rules by the two legislative bodies as "nonjusticable" because the Constitution gives them clear authority in that area. That is what Slaughter and Pelosi are counting on. Weather there are limits to the discretion that the SCOTUS will allow is what will be tested.
With the current makeup of the court, I believe that they would hear the case and strike it down, but what will be the makeup of the court if and when they do hear the case?
I also wouldn't rule out the idea of court packing (ala FDR) with this group of libs in power...