"I'm really disappointed that I had to file cloture to stop a Republican filibuster on this worthy legislation, but I did," said Reid of the bill that was originally penned by Republican Sen. Scott Brown (Mass.) and Democrat Kirsten GillibrandKirsten Elizabeth GillibrandTrump thinks he could easily beat Sanders in 2020 match-up: report Listen: EMILY’s List upbeat about Dem House in '19 Desperate Democrats shouldn't settle for Oprah MORE (N.Y.). "They're not going to let us move to this. We had to file cloture to stop this filibuster … I repeat, it is too bad we had to file cloture." 

A senior Republican aide, however, shot back on Monday that Reid had not checked in with Minority Leader Mitch McConnelll's (Ky.) office to see if any of any GOP members had objections, and suggested Republicans were mystified on why Democratic leadership filed cloture. 

“Sen. Reid didn’t even check in with us before filing cloture so it came as a surprise when he did it,” he said.

Reid filed for cloture before adjourning the Senate on Friday, which would generally indicate that at least one senator had objected to allowing Democratic leadership to bring the bill to the floor for debate. Reid's move set up the 5:30 p.m. vote for Monday which could allow the legislation on the Senate floor. 

The majority leader assured his colleagues that the legislation would move despite the Republican objection or objections and indicated he would allow an open amendment process, a practice that became scarce in the Senate in the later months of 2012. 

"When we get on this bill — and we will get on this bill — we're going to have an amendment process," he said. "It is my wish that the Republicans will not abuse the rules in the Senate."

–This story was updated at 3:31 p.m.