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“Her issue at the time was that Majority Leader Reid had said he would not allow any Republican amendments to the bill at the time. She was opposed to that process, which shut Republicans out of the debate,” he said.

Reid spokesman Jim Manley said that, this time around, Ms. Collins would get her wish.

Surrounded by more than a dozen Democrats on Thursday, Mr. Lieberman made the case that if they can get passed the procedural hurdles related to amendments that lawmakers corral the 60 votes, including Ms. Collins and Sen. Richard G. Lugar, Indiana Republican, needed this time to overcome Republican objections and advance the bill to the floor.

“The only reason not to get this bill done this year is a reluctance to spend the time to do it and that is just an unacceptable excuse,” Mr. Lieberman said.