Washington (CNN) A much-anticipated Senate debate on immigration this week seemed to stutter even before it began Tuesday, as negotiations devolved into a fight about process and a healthy round of finger pointing, with time to reach a deal before the end of the week evaporating with each passing hour.

At the core of the debate was the realization dawning on both sides that even after weeks of lead-up, no proposal seemed to have the key number of 60 senators supporting it -- the threshold to advance that proposal in the Senate, if it is ever able to kick off.

In the Capitol on Tuesday, no one could say exactly how things were going to go, with everyone banking on a last-minute deal being struck, as negotiations continued furiously in the background. On Tuesday evening, McConnell ended the drama for the day, teeing up a final vote on whether to even open debate on the bill for Wednesday.

"It's amazing how magically, suddenly things appear," Florida Democrat Bill Nelson said when asked about criticism that Democrats and bipartisan negotiations have yet to produce a deal with 60 votes.

Senate No. 2 Democrat Dick Durbin of Illinois said the holdup was "reaching agreements."

"You're supposed to be confused. You are on the outside," he told reporters Tuesday afternoon. "I'm on the inside and I'm confused."

Finger pointing

The process got off to an inauspicious start on Monday night, when the Senate cleared a procedural hurdle to move toward opening debate on the expiring Deferred Action for Childhood Arrivals program, as had been promised for weeks by Senate Majority Leader Mitch McConnell of Kentucky. But just outside the Senate chamber, Republican leadership told reporters that the debate would get only a week of floor time -- a move to pressure Democrats to produce their legislative proposals.

Democrats and some Republicans had anticipated possible weeks of debate -- and little legislation has been finalized and introduced on either side yet that would deal with DACA, a program that protected young undocumented immigrants from deportation that President Donald Trump is ending, and any other provisions on immigration.

Instead of then moving straight into a vote to open debate, the Senate spent Tuesday arguing about next steps, with Democrats accusing Republicans of tampering with the procedure and Republicans accusing Democrats of dilatory tactics because they had nothing to offer.

The finger pointing spilled onto the Senate floor Tuesday afternoon, when McConnell moved to consider an amendment that would have dealt with sanctuary cities -- a favorite target of Republicans.

Schumer noted that neither would likely succeed -- but would at least kick things off. And he noted that only one had been drafted and officially introduced -- the McCain-Coons bill -- saying the Senate could vote as soon as the Republican proposal was written. Some Democrats also privately suspected Republicans were hesitating to have the White House proposal go first, only to be defeated immediately, and were seeking to delay.

"That (pairing) will tell us, sort of, the bounds," Schumer told reporters at a news conference later. "I don't think either of them will get large bipartisan support. But it will give us an idea of the parameters and can set us moving. ... Now, if these proposals fail, the body will continue to work its bipartisan will for a bill that can pass."

Republicans, meanwhile, mocked Democrats for not being ready in time and trying to avoid votes that could be difficult for vulnerable members of their party.

"It's an open process, right?" said GOP leadership member Sen. John Thune of South Dakota. "So if our leader wants to call that (sanctuary cities) amendment up, I mean, eventually we'll get to (the White House framework), but there are others we want to process as well, but I'm not sure why you would block even moving to the initial consideration of amendments, which is what the Democrats are currently doing. That makes no sense if you're the ones who have been advocating now for literally weeks that we need to get on an immigration bill."

Calm exterior but negotiations continue

Democrats did not telegraph any concern about the timeline, even as the day slipped away. They called a Thursday deadline "arbitrary," in the words of Sen. Bob Menendez of New Jersey, and held their fire on GOP leadership.

"Negotiations continue," Durbin said. "The timetable is dependent on the rules of the Senate and unanimous consent requests. ... I hope we can finish it this week."

"The sooner, the better," Schumer said at a news conference after party lunches. "But right now, our focus is getting to 60. That's going to take a lot of push and pull. A lot of compromise."

The calmness, though, belied furious negotiations behind the scenes.

As Democrats were locked away in their closed-door lunch, intense conversations among key players spilled outside into the view of reporters.

At the top of the caucus meeting, Durbin and Schumer huddled for a few minutes with two aides on the steps just outside, where press is not allowed, an unusual occurrence. Not long after going inside, Schumer came out again and huddled with just the staff, which included top Durbin counsel Joseph Zogby, a regular attendee at immigration meetings. After Schumer returned to his meeting, the staff continued to meet just outside.

Democrats were tight-lipped coming out of the meeting -- Sen. Chris Van Hollen of Maryland confirmed they were going over proposals on immigration and Sen. Tim Kaine of Virginia said they were "making progress," but all refused to go into further detail.

A group of bipartisan senators also continued to work furiously behind-the-scenes, exchanging drafts of possibilities and working to find a fit that would get 60 votes.

Coons, who is part of the group as well as being involved in the McCain-Coons bill, was working the Senate gym Tuesday morning, talking to members about the negotiations, according to a source familiar. The bipartisan gathering place had a fair number of Republicans and Democrats in it as Coons spoke to those around the room, the source said.

Of course, in the Senate, things could come together very quickly -- or not at all. In the meantime, everyone was waiting to see what happened next.

Asked if he felt that he was getting what was promised, Durbin was characteristically upbeat.

"It does," Durbin said. "This is the Senate."