Didn't the Republicans do something similar last term?
It happened here in PA when the Dems had a one seat majority but couldn't get their leader elected. As a result, Republican Denny O'Brien was elected as a compromise choice.
He received six Republican votes and all but three Dem votes. The six Republicans that voted for him were some of the most conservative members of the body so he had very broad support.
This isn't exactly the same though since the Dems were in the majority here in PA when they pulled that move.