Georgia Republican Saxby Chambliss is among a group of Senators pushing a bill to keep the Guantanamo Bay prison open.
The detention facility off the island of Cuba holds terrorism suspects.
The Obama Administration has committed to closing Guantanamo and moving high-value detainees to prisons in the U.S.
Meanwhile, the House Armed Services Committee is backing limits on President Barack Obama's authority to transfer terrorist suspects from the prison at Guantanamo Bay, Cuba, to foreign countries.
On Thursday, members rejected an amendment to undo the limits.
The panel's top Democrat, Rep. Adam Smith of Washington state, sponsored the amendment, saying the U.S. shouldn't hold low-level terrorists for an undetermined period of time.