Under the state constitution the legislature has the power to call for a special session but I don't think they have the votes.
That is my understanding of the conventional theory, as well, they need all R’s and even a few D’s to get to 60%, based on various reports.
But I’ve also heard some legal analysis that said they may only need 51% to open a session under their potentially separate power of the US Constitution.
This would have to go to the US Supreme court if course, but it would almost start there.