The White House said any deal must include $25 billion in funding for the border wall, the central plank of Trump's presidential campaign.
Senior White House officials said the plan was a compromise that could win support from both parties and enough votes to pass the Senate.
Thursday the White House announced its new immigration framework, an offer that would grant a pathway to citizenship for almost 2 million so-called dreamers.
"The framework released by the administration Thursday includes a "$25 billion trust fund for the border wall system, ports of entry/exit, and northern border improvements and enhancements", a limitation of family reunification to spouses and minor children, and a "10-12 year path to citizenship, with requirements for work, education and good moral character" for those already registered or eligible for the rescinded Deferred Action for Childhood Arrivals program.
According to Trump's proposal, the undocumented immigrants could become United States citizens over a 10 to 12 year period if they met certain requirements.
The plan would also end the diversity visa lottery program. But President Trump's designs for undocumented parents are not the only troubling aspect of this proposal.
I am not personally invested in the fate of the Dreamers, but I think it is the right thing to provide them with legal protection and a path to citizenship.
The Statue of Liberty, a USA symbol of immigration, stands in New York Harbor at sunset in New York City.
Trump has also argued for ending "chain" migration, the practice of allowing the extended family members of people who already have USA citizenship to immigrate.
Senate Minority Whip Dick Durbin (D-Ill.) blasted an immigration reform framework proposal put forth by the Trump administration on Thursday.
The Obama-era DACA programme was ended by Trump last September.
By ending DACA, Trump helped move immigration to the forefront, Westerman said.
"I get scared and anxious but I have had nothing but support through this", she said.
"I'm optimistic these ongoing negotiations will lead to results", Republican Senate Majority Leader Mitch McConnell said of talks involving a group of about three dozen senators trying to hammer out a deal to protect about 700,000 Dreamers from deportation.
White House officials said that the list of enhanced security measures - which have been on anti-immigration wish lists for decades - were nonnegotiable.
The call grew contentious, some of the sources said, when Miller began to solicit input from the conservative immigration groups, many of which have long advocated restrictions on legal immigration and no amnesty for undocumented immigrants now in the United States.
He said in a statement that this plan is generous and humane while also being responsible.
The plan would provide an eventual path to citizenship for approximately 1.8 million individuals now living illegally in the country.
Cruz did not mention Trump by name, but there is no doubt that he was voicing the concern shared by numerous men and women who supported Trump in the last presidential election.
"Chain migration, visa lotteries that don't work, a lot of these situations have to be remedied before we can solve the problem because otherwise the problem's just gonna materialize again", Davidiuk said. Arkansas Senator Tom Cotton is someone who's always been pushing for these changes to legal immigration that are included in this framework.
That could make the plan hard to get past Democrats, no matter how strong they want the Dreamers reform.
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Because I'm anxious that, it looks like a hamstring. "We're working hard and we'll keep trying to get someone". Cressy is okay, but it's more the Lanzini one that we're anxious about.
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