Sen. Jeff Flake Jeffrey (Jeff) Lane FlakeHow fast population growth made Arizona a swing state Jeff Flake: Republicans 'should hold the same position' on SCOTUS vacancy as 2016 Republican former Michigan governor says he's voting for Biden MORE (R-Ariz.) said on Wednesday that he has secured a promise from Majority Leader Mitch McConnell Addison (Mitch) Mitchell McConnellFEC flags McConnell campaign over suspected accounting errors Poll: 59 percent think president elected in November should name next Supreme Court justice Mark Kelly: Arizona Senate race winner should be sworn in 'promptly' MORE (R-Ky.) to bring up a legislative fix for a key Obama-era immigration program next month.

“I am ... pleased that the Majority Leader has committed to bring the bipartisan DACA bill we are currently negotiating to the Senate floor in January," Flake said in a statement, referring to the Deferred Action for Childhood Arrivals program.

Flake's statement comes after he predicted early Wednesday morning that a bill would come up on the Senate floor next month, as lawmakers appear increasingly likely to punt the fight to next year.

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McConnell A spokesman fordidn't immediately respond to a request for comment, but told The Hill earlier Wednesday that he didn't have any scheduling announcements yet for January.

The Trump administration has announced it will end DACA, which allows immigrants brought into the country illegally as children to work and go to school.

Congress faces a mid-March deadline to pass legislation addressing the program or hundreds of thousands of immigrants will be at risk of deportation.

John Kelly John Francis KellyMORE Flake is part of a bipartisan group of senators that have been negotiating an agreement that would link DACA to a border security package. Several key senators met with White House chief of staff on Tuesday to discuss the program.

Some Democrats and immigration activists have been demanding that a deal gets passed this year and viewed the end-of-the-year spending bill as their best shot.

But key senators in both parties have signaled that it is increasingly unlikely as Congress appears ready to leave town this week until January.