The Senate's Republican leadership set Friday as the deadline for striking a deal, and Thursday was shaping up to be a day of consequential votes in the chamber on competing immigration plans, including the president's.
The key will be which of the plans can receive 60 votes, the threshold for advancing legislation in the closely divided 100-member Senate.
The bipartisan measure, which has eight Republican and eight Democratic sponsors, emerged from a centrist group nicknamed the "common sense coalition."
"Our legislation underscores the broad, bipartisan commitment to creating a path to citizenship for Dreamers, who were brought to this country illegally through no decision of their own, while strengthening border security to help stop the flow of illegal immigrants,"Senator Susan Collins, a Republican founder of the coalition, said in a statement announcing the measure.
The president's plan protects Dreamers and boosts border security funding, but also abolishes the diversity visa lottery and restricts family reunification, a policy Trump calls "chain migration."
The bipartisan effort would only make limited changes to family reunification, and would leave the diversity lottery untouched, because it is too "politically toxic," Republican Senator Lindsey Graham said.
Graham said there was "growing consensus" around the plan.
"I think that's got the best chance of getting 60" votes, he told AFP.
But supporting the compromise would put members of Trump's own party at odds with the president, who urged senators to oppose any bipartisan plans that were different from his own.
In a statement, the president called on all senators to "oppose any legislation" that fails to address what he calls the "four pillars" in his plan.
"That includes opposing any short-term 'Band-Aid' approach," he said.
The remark had brought action in the Senate to a virtual standstill, and raised prospects that the chamber would miss its self-imposed deadline on immigration.
Time is an increasingly important factor. Lawmakers for months have struggled to craft a compromise after Trump scrapped a program that allowed Dreamers 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 -- plus 1.1 million others who were eligible but did not sign up -- could begin to face deportation by that date if no fix is in place.
The Senate is expected to consider four plans Thursday: The president's; a Republican bill dealing with "sanctuary cities" which defy federal orders on illegal immigrants; a measure by Republican Senator John McCain and Democrat Chris Coons that addresses DACA and border security but not broader immigration policy; and the bipartisan compromise.
Top Republicans said Trump's plan has the best shot at becoming law out of those being considered. But Democrats have panned it, making it highly unlikely that it would garner enough votes to pass.
In the midst of the showdown, Democrats stressed Trump would be to blame for any failure to reach a deal.
Americans "know this president not only created the problem, but seems to be against every solution that might pass because it isn't 100 percent of what he wants," top Senate Democrat Chuck Schumer said.
"If, at the end of the week, we are unable to find a bill that can pass... the responsibility will fall entirely on the president's shoulders and those in this body who went along with him."
The Senate is not the only hurdle. Any immigration deal would have to also clear the House, where conservatives bridle at the thought of providing "amnesty" to millions of immigrants, and ultimately pass muster with Trump.
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