Story highlights Republicans met Monday in advance of Tuesday's meeting with the President

That meeting included Department of Homeland Security Secretary Kirstjen Nielsen

Washington (CNN) President Donald Trump called on bipartisan lawmakers Tuesday to both come up with "a bill of love" to keep thousands of young undocumented immigrants from having to leave the country but also deliver on his campaign promise of a wall and border security, in a wide-ranging meeting that played in full view of the public.

The goal of the White House meeting was to discuss how to reach an agreement between Democrats and Republicans, while still accomplishing the President's push for a wall along the US border with Mexico and other changes to the US immigration system -- something Democrats widely oppose.

In the background, details are still being worked out on what a plan to help recipients of the Deferred Action for Childhood Arrivals program, would look like, and a bipartisan group of Senate lawmakers led by Democrat Dick Durbin of Illinois and Republican Lindsey Graham of South Carolina continues to negotiate.

Following the meeting, Durbin said he was pleased by the "sense of urgency" by the participants and that they "narrowed down the list of what they are going to discuss in the first phase of immigration, the DACA phase, to border security, chain migration and the diversity visa."

Speaking in the Cabinet Room in the White House with Republican and Democratic lawmakers, Trump urged people to "put country before party" but said he would not protect hundreds of thousands of young undocumented immigrants from deportation without funding for a border wall and a series of immigration changes.

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