House spokesman Brad Miller said Republican Cliff Rosenberger's interim replacement will be picked Tuesday. House Democrats say acting House leader Kirk Schuring isn't eligible to add session days under a House rule that says only the speaker can do so.
Miller said that is superseded by a constitutional mandate that the House meet every five days.
The rules dispute adds to a process that's already been rocky. Republicans hit an impasse last week when none of the three candidates to fill Rosenberger's unexpired term could secure the 50 votes needed.
Miller says GOP Finance Chairman Ryan Smith now has the votes.