Obama instituted the program to protect young people whose parents brought them into the country as minors when they entered the US without legal permission.
Advocates around the country have rallied to urge passage of the DREAM Act - the Development, Relief and Education for Alien Minors Act - to provide a pathway to citizenship for DACA beneficiaries. Wall funding wasn't included in a stopgap year-end funding bill, nor was it ever considered when Democrats thought they'd struck a deal on DACA with Trump this fall.
For more than a year, Republicans have tried to downplay Trump's border wall, ignore it, even blast it. Members of the GOP who have spent decades on immigration reform have reiterated time and time again that a border wall is hardly the most effective way to secure the border.
On Tuesday, U.S. District Judge William Alsup granted a request by California and other plaintiffs to prevent Trump from ending the Deferred Action for Childhood Arrivals program while their lawsuits play out in court.
A key Senate Republican, Texas Senator John Cornyn, said, "I do want us to get to a solution". "The wall is going to happen, or we're not going to have DACA".
Trump last week asked Congress for $18 billion for the first phase of the wall along the border with Mexico, whose officials said they will not pay for the barrier.
Ultimately, the meeting concluded with a two-phase solution that pairs a DACA bill with funds for the wall and punts comprehensive immigration reform to Congress at a later date.
Trump: Wall 'Must' Be Part of Any DACA Deal
The top Democrat in the House of Representatives, Minority Leader Nancy Pelosi, told reporters Monday, "I think we will" reach an agreement on the young immigrants, mainly because neither Democrats nor Republicans want a partial government shutdown at the end of next week.
King said Trump should force Democrats to give in to stricter border security demands, or reap the consequences of failing to follow through on his campaign promises.
Since so many Americans agree on their contributions to the country, fixing the program that protects them "should be easy", he said, but instead "these young people find themselves stuck in the middle of a much broader debate about border walls, national security and the inner workings of our visa system".
"I hear so much about earmarks - the old earmark system - how there was a great friendliness when you had earmarks", Trump quipped.
"An issue of this magnitude must go through the normal legislative process", White House spokeswoman Sarah Sanders said in a statement.
Rep. Steny Hoyer, D-Md., right, listens as President Donald Trump speaks during a meeting with lawmakers on immigration policy in the Cabinet Room of the White House, Tuesday, Jan. 9, 2018, in Washington.
"To throw down a list from the hard, hard-line wing of the White House is not a very fortuitous or smart thing to do", he added.