I am not sure they would. I think they might kick it to the House. The jurisdiction of the court over the election process for this would be questionable in my mind.
Then we disagree, on two grounds. I believe that deciding constitutionality is the strict provence of the Court. I also believe the court is jealous of that power and is unlikely to want to share it with the House.
Besides, the temptation to meddle in the process would just be tooooooo tempting to certain activists on the SC...