At the time, Schumer and House Minority Leader Nancy Pelosi said that they hoped to finalize a deal with Trump to protect DACA recipients "as soon as possible" and maintained that both sides agreed that a border wall would not be part of it.
And he hopes to prevent immigrants from sponsoring extended family members to move to the U.S., limiting green cards to spouses and children.
Border wall funding in particular was ruled out during a previous discussion with Trump, the lawmakers added.
Instead, the White House list includes longstanding demands of the Republican Party's immigration hardliners, including expediting removals of unaccompanied children arriving at the border; tightening standards for people allowed to seek asylum in the US; barring immigrants who have been convicted of a range of crimes, including drunk driving; and barring federal grants to so-called "sanctuary cities" that do not turn over illegal immigrants to federal authorities.
About 690,000 immigrants are enrolled in DACA, but their work permits are set to begin expiring in March.
Trump phased out the program last month and gave Congress six months to find an alternative bill to the policy. Implemented under former President Barack Obama, the initiative has allowed about 800,000 beneficiaries, known as Dreamers, to live and work in the USA on renewable authorizations. "Allowing extreme factions within the administration to undermine the president's solid word of commitment to Dreamers would put an end to the most passable immigration reform proposal we've seen come out of Congress in decades", said Ali Noorani, executive director of the National Immigration Forum, an immigration advocacy group.
In responding to a question about how the Dreamers fit into the United States' future workforce, Trump also called for comprehensive immigration reform.
Trump's tense relationship with Tillerson burst into public view last week.
"These are reasonable proposals that will build on the early success of President Trump's leadership".
The president has previously insisted the wall will go ahead and that he wants "massive border security" in exchange for a deal on DACA protections.
Her comments about DACA largely echo what President Trump has said about the program.
Trump said in a letter to Congress on Sunday that former President Barack Obama's establishment of DACA "bypassed the Congress" and "threatened Congress's status as a coequal branch of Government", resulting in what he characterized as a surge of illegal immigration.
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