The immigration overhaul would end so-called "chain migration" in the green card program by limiting who US citizens can sponsor to only spouses and minor children.
The White House is also demanding the use of the E-Verify program by companies to keep illegal immigrants from getting jobs, an end to people bringing their extended family into the United States, and a hardening of the border against thousands of children fleeing violence in Central America.
About 690,000 immigrants are enrolled in DACA, but their work permits are set to begin expiring in March.
On Oct. 8, the Trump administration provided a list of conditions for any congressional legislation that offered protections against deportation for DACA recipients, who were brought to the US before turning 16-years-old. That's the program known as DACA that shields from deportation undocumented immigrants who were brought to the country as children.
Donald Trump has proposed a merit-based immigration system that could benefit highly- skilled Indian workers but prevents them from sponsoring their extended families, as part-of an aggressive plan which the United States president said will serve national interest.
But the president has long made a wall the centerpiece of his immigration reform, insisting it must be a part of any legislation to protect dreamers like Greisa Martinez Rosa from deportation.
Also on the list is cracking down on sanctuary cities, curbing the number of unaccompanied minors entering the US, and limiting legal immigration.
"With the leadership of President Trump and Vice President Pence, we will work together to address our country's immigration crisis and issues surrounding it like DACA, sanctuary cities, chain migration and the flow of illegal drugs", Rokita said in the statement.
Trump's tense relationship with Tillerson burst into public view last week.
In a joint statement Sunday night, Pelosi and Schumer said Trump's list of proposals failed "to represent any attempt at compromise".
Democratic leaders in the House and the Senate were quick to condemn the list.
Mr. Schumer and Mrs. Pelosi, who received the immigration principles on Sunday, reacted with dismay. "We told the President at our meeting that we were open to reasonable border security measures. but this list goes far beyond what is reasonable".