As they begin to plan their opening steps in the new majority, a growing number of Republican senators are expressing deep reservations about changing Senate rules back to the old system in which 60 votes were needed to overcome filibusters on presidential nominees. Instead, a number of senior GOP senators like Orrin Hatch of Utah and even junior Republicans like Ted Cruz of Texas are signaling privately and publicly that they want to stay at the 50-vote threshold set by Reid’s Democratic Senate majority.

How Republicans resolve the issue will have major consequences for President Barack Obama’s Cabinet and judicial nominees, with a defense secretary and attorney general slated for confirmation votes in the next Congress along with scores of federal judges. The closed-door GOP debate over the potent delaying tactic is scheduled to take place Tuesday with the new Republican freshman class.

Behind the scenes, the debate has been intensifying for days.