Lawmakers have spoken for months about the need to craft a bipartisan compromise after Trump scrapped a program that allowed so-called Dreamers brought to the United States illegally as children to stay, and gave Congress until March 5 to find a solution.
Some 690,000 Dreamers registered under the Obama-era Deferred Action for Childhood Arrivals (DACA) program, and 1.1 million others were eligible but did not sign up.
Last month, Trump introduced a proposal that would put all 1.8 million of them on a pathway to citizenship, in exchange for stiff cutbacks on overall immigration and funding for a massive wall on the US border with Mexico.
Senate Republicans transforming that plan into legislation say it has the best chance of becoming law.
But Republicans who control the Senate need Democratic votes to get an immigration bill across the finish line, and the opposition party has panned the presidential plan, arguing for a narrower measure that addresses the Dreamers and border security.
A bipartisan solution -- and one that would gain the 60 votes necessary to advance legislation in the 100-member Senate -- has proven elusive.
Senate Majority Leader Mitch McConnell promised Republicans and Democrats a week of rare open-ended debate in which they could introduce immigration-related measures.
'The sooner, the better'
By Tuesday, Senate floor action was gummed up by procedural hurdles, as both parties failed to agree on the opening amendments to debate.
"The sooner we get started the better, because we'll need to wrap this up this week," McConnell warned, citing the need to move on to other legislative priorities.
"Senators have had plenty of time to prepare."
The president weighed in, heaping pressure on both sides.
"Wouldn't it be great if we could finally, after so many years, solve the DACA puzzle," Trump tweeted Tuesday. "This will be our last chance, there will never be another opportunity!"
Lawmakers scrambled to find a path forward.
"If there's no deal by the end of the week then that, I think, leaves the DACA recipients in some jeopardy," Senate Republican John Cornyn said.
Wednesday promised to be an intense day of haggling, and possibly voting, in the Senate as the two parties sought a deal.
"If we can come up with a bipartisan compromise that's right in the ballpark of 60, then let it rip, let's go," top Senate Democrat Chuck Schumer told reporters.
Republican Senator John Thune said he believed "something will eventually move," but that success was far from assured.
"Getting 60 is going to be a challenge for the propsals that are out there right now," he said.
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