Washington (CNN) The Senate is set to begin debating immigration Monday evening, and in a rare occurrence for the upper chamber of Congress, no one is quite sure how that will go.

The historic debate on the status of 11 million undocumented immigrants and future of legal immigration comes as President Donald Trump has vowed to end the Deferred Action for Childhood Arrivals program, which protected young undocumented immigrants who came to the US as children from deportation, next month.

Let the debate begin

At 5:30 p.m. ET Monday, senators will vote on whether to open debate on the bill, a vote that is largely expected to succeed.

From there, a lot will be up to senators. Both sides will be able to offer amendments that will compete for 60 votes -- the threshold to advance legislation in the Senate. It's expected that amendments will be subject to that threshold and will require consent agreements from senators for votes, opening up the process to negotiations.

If a proposal can garner 60 votes, it will likely pass the Senate, but it will still face an uncertain fate. The House Republican leadership has made no commitment to consider the Senate bill or hold a debate of its own, and House Speaker Paul Ryan has pledged repeatedly to consider a bill only if Trump will sign it.

Late Sunday, a group of Republicans introduced a version of Trump's proposal on DACA as an amendment.

Different groups have been working to prepare legislation for the immigration effort, including the conservatives who worked off the White House framework and a group of bipartisan senators who have been meeting nearly daily to try to reach agreement on the issue. Trump has proposed giving 1.8 million young undocumented immigrants a pathway to citizenship in exchange for $25 billion for his long-promised border wall and a host of other strict immigration reforms.

Trump spoke about his priorities Monday, during a White House event where he unveiled his plans for infrastructure. He said any deal would require "tremendous border security" and that Republicans wanted an agreement.

"I can tell you, speaking for the Republican Party, we would love to do DACA. We would love to get it done," he said. "I think there is a good chance to get DACA done if the Democrats are serious and really want to do it."

Trump also repeated his push to put pressure on Democrats over immigration.

"I hope the Democrats are not going to use it just as a campaign. You know, they've been talking about DACA for many years, and they haven't produced," he said. "We started talking about DACA, and I think we'll produce. But if the Democrats want to make a deal, it's really up to them."

The bill from GOP senators largely sticks to those bullet points, including sharp cuts to family-based migration, ending the diversity lottery and giving federal authorities enhanced deportation and detention powers.

Alternatives from moderates

A bipartisan group of about 20 senators was drafting legislation over the weekend to offer perhaps multiple amendments and potentially keep the debate focused on a narrow DACA-border security bill.

Multiple members of the group have expressed confidence that only such a narrow approach could pass the Senate -- and hope that a strong vote could move Trump to endorse the approach and pave the way for passage in the House.

Advocates on the left may offer a clean DACA fix, like the DREAM Act, as well as the conservative White House proposal -- though neither is expected to have 60 votes.

The move to hold an unpredictable Senate debate next week fulfills the promise Senate Majority Leader Mitch McConnell made on the Senate floor to end the last government shutdown in mid-January, when he pledged to hold a neutral debate on the immigration issue that was "fair to all sides."

Even Sunday, leadership aides weren't able to say entirely how the week would go. The debate could easily go beyond one week, and with a scheduled recess coming next week, it could stretch on through February or even longer.

One Democratic aide said there will likely be an effort to reach an agreement between Republicans and Democrats on timing so that amendments can be dealt with efficiently, and, absent that, alternating proposals may be considered under time-consuming procedural steps.

"We just have to see how the week goes and how high the level of cooperation is," the aide said.

Many Democrats and moderate Republicans were placing hope in the bipartisan group's progress.

"We're waiting for the moderates to see if they can produce a bill," said the Senate's No. 2 Democrat, Dick Durbin, on Thursday. "And considering options, there are lots of them, on the Democratic side. There's no understanding now about the first Democratic amendment."

Durbin said traditionally both sides have shared a few amendments with each other to begin to figure out the process' structure. He also said the bipartisan group could be an influential voting bloc, if they can work together.

"They could be the deciding factor, and I've been hopeful that they would be, because I've had friends in those Common Sense (Coalition), whatever they call themselves, and reported back the conversations, and I think they're on the right track."

As she was leaving the Senate floor Friday night after the Senate voted to pass a budget deal and fund government into March, Maine Republican Sen. Susan Collins was optimistic about the preparedness of the bipartisan group she has been leading for the all-Senate debate.

"We'll be ready," she told reporters.

Oklahoma Republican Sen. James Lankford, who has been working both with the group introducing the White House proposal and the bipartisan group, said late Friday night that his plan is "to get things done."

"It's no grand secret that I have no problem with the President's proposal; the challenge is going to be trying to get 60 votes," Lankford said. "So I would have no issue with what (Sens. John) Cornyn and (Chuck) Grassley are working on and with the President supporting that, but I also want to continue to try finding out and see, if that doesn't get 60 votes, what could."

He said everyone is waiting to find out what happens next.

"Everybody's trying to figure out the chaos of next week, and I'm with you," Lankford said. "I don't know yet how open the process is going to be. I hope it's very open."