Sen. Roger WickerRoger WickerAs US healthcare changes, preventative screenings can't stop A guide to the committees: Senate Pruitt confirmation sets stage for Trump EPA assault MORE (R-Miss.) on Wednesday blasted Senate Majority Leader Harry ReidHarry ReidThis obscure Senate rule could let VP Mike Pence fully repeal ObamaCare once and for all Sharron Angle to challenge GOP rep in Nevada Fox's Watters asks Trump whom he would fire: Baldwin, Schumer or Zucker MORE's (D-Nev.) management of the upper chamber.

Wicker said that the energy efficiency bill that failed to clear a GOP filibuster earlier this week illustrated the problem. Republicans had demanded amendment votes in exchange for passage of the bipartisan energy efficiency bill sponsored by Sens. Jeanne Shaheen (D-N.H.) and Rob Portman (R-Ohio), but Reid refused. 

Reid has said that the GOP had backtracked on a previous agreement to pass the bill for a vote on constructing the Keystone XL pipeline.

Wicker said Reid had continually obstructed opportunities for Senate Republicans to offer amendments.

"A popular piece of legislation on energy efficiency was derailed by the majority leader's resistance to the open amendment process," Wicker said.

Wicker said that senators should be free to offer amendments.

"What has become of the United States Senate under this Harry Reid gag rule is unconscionable," Wicker said. "It should be reversed, and senators of both parties should stand in resistance to the idea that we cannot offer amendments and have them debated as they've always been debated in the United States Senate."

The Mississippi Republican claimed that Reid had used a procedural tactic, known as "filling the amendment tree," to block consideration of amendments more times than his predecessors. Wicker further argued that Reid was stifling Senate Republicans' minority rights and, by extension, the Senate's functioning.

"Its current abuse undermines the Senate's ability to address pressing national issues and to carry on the tradition of debate that has always defined this body. That can really not be denied," Wicker said.