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 along the US-Mexico border and a series of immigration changes.
Trump said his version of a "clean" deal would include DACA, border security, ending "chain migration" or family-based migration, and ending the diversity visa lottery.
Schumer said Tuesday that the Republican president's "tone was very good" and that it was "encouraging that the president seems open to a narrow deal" to protect immigrants brought to the US illegally as children. Trump past year ended the Obama-era Deferred Action for Childhood Arrivals program, which shielded more than 700,000 people from deportation and gave then the right to work legally.
On Tuesday, Trump said he a "permanent" solution was needed for the Dreamers, but also insisted on the importance of border security, especially with Mexico.
Some immigration advocates agreed that a deal would likely involve boosted border security, including some measures to buttress physical barriers such as reinforcing fences and augmenting other existing structures.
According to reports, Donald Trump is set to meet with developers to begin looking at different prototype concepts for his border wall following his upcoming State of the Union address. "We really want to work it out", Mr Trump said ahead of a meeting with Republican senators.
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President Donald Trump appeared to contradict himself multiple times in a meeting on immigration with a bipartisan group of lawmakers Tuesday - a reflection of growing frustration from Capitol Hill about the lack of direction from the White House on the issue.
Conservatives quickly sounded alarms about a process that would lead to a comprehensive agreement on immigration, a path that has always been anathema to many rank-and-file Republicans. "I'll take all the heat you want to give me, and I'll take the heat off both the Democrats and the Republicans".
"We don't oppose building a wall, but that's certainly not our first priority", said Eric Ruark, director of research at NumbersUSA.
"So, that's I think the picture that we need to be looking through, the lens we need to be looking through, not only what can we agree to among ourselves on a bipartisan basis, but what will you sign into law", Cornyn said. Trump added if the group presents him with a plan he does not like he would support it anyway.
His concern is about efforts by Trump and some congressional lawmakers to include issues not related to immigrants brought into this country by their parents as children who were covered under the program Trump scuttled in September.
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.