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WASHINGTON (CNN) – After two days of procedural fits and starts, the Senate finally moved Wednesday to begin debate on immigration reforms aimed at resolving what to do with undocumented immigrants who came to the US as children whose legal status in the country may soon expire.

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The Senate approved a motion by voice vote to begin debate, and as they were doing so, a group of Republican senators said there was a possible deal in sight.

Democrats demanded the debate on immigration — and even briefly shut down the government to try to force it — but have yet to agree to a compromise bill with a group of Republicans that could get 60 to pass the chamber.

Those talks were still underway in the office of Sen. Susan Collins, R-Maine, when the floor debate formally opened. Members emerged from Collins’ office and said they had the contours of an agreement that would be “two pillars.” It would protect DACA recipients in exchange for a major boost in border security.

Sen. Jeff Flake, R-Arizona, told reporters that he expects the bipartisan coalition would have a finished proposal to announce Wednesday, a major breakthrough after weeks of negotiations.

“Seems to me the consensus is to have big border security and big DACA,” said Sen. Lindsey Graham, R-South Carolina.

But Graham told reporters that any deal would not include a pathway for the parents of DACA recipients.

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“If you deal with the parents now you lose a lot of Republicans. If you try to do the breaking chain migration now you lose a lot of Democrats,” said Graham.

“It would be a two-pillar bill,” he added.

It’s still unclear if the bipartisan approach would be able to garner the needed 60 votes to pass, however.

Senate Majority Leader Mitch McConnell explained why he supports a “four pillars’ approach, addressing problems of both illegal and legal immigration.

“Common sense dictates we cannot simply treat one symptom of our broken immigration policy in complete isolation. We must address the underlying problems as well,” he said. “That means fixing broken parts of our legal immigration system.”

President Donald Trump has been clear that he doesn’t want anything short of a four-pillar solution – one that includes border security, protections for DACA recipients, an end to the diversity lottery and a massive overhaul of the country’s legal immigration system.

The inability of the bipartisan group to put a bill on the floor for a vote has frustrated Republicans who said they were stunned that after months of negotiations, the group wasn’t ready. Many Republicans back a plan that is supported by Trump, which would lead to a pathway for citizenship for 1.8 million people in return for $25 billion for border protection and significant changes to “chain” migration and the diversity visa lottery. That measure is also unlikely to get 60 votes.

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