President Donald Trump will back a path to citizenship for 1.8 million young undocumented immigrants who were either shielded by an Obama-era program or eligible for it, a Republican source told CNBC on Thursday.

White House policy aide Stephen Miller described the administration's upcoming immigration plan in a conference call, NBC News first reported. The White House is set to release its proposal on Monday.

The plan will also call for a $25 billion "trust fund" for the president's proposed border wall, the source said. It will call to limit family migration and end the visa "lottery" system.

Trump ended the Obama-era Deferred Action for Childhood Arrivals program, and it starts to phase out March 5. Senate Majority Leader Mitch McConnell has pledged to bring an immigration bill to the floor by the next government funding deadline on Feb. 8, even if lawmakers do not strike a deal before then.

McConnell said in a statement that he hopes the White House plan will provide guidance for the Senate as they continue to work towards an agreement. A spokesman for House Speaker Paul Ryan told CNBC, "We're grateful for the president showing leadership on this issue and believe his ideas will help us ultimately reach a balanced solution."

In an outline released later Thursday, the White House said its proposal would include a 10 to 12 year path to citizenship, "with requirements for work, education and good moral character." It also calls for a curb to family migration by limiting family sponsorships to "spouses and minor children only."

GOP Trump allies in the Senate like Sen. Tom Cotton of Arkansas and David Perdue of Georgia praised the plan. But concerns quickly emerged, both on the left and right flank.

Sen. Dick Durbin, D-Ill., who helped to craft a bipartisan Senate proposal Trump rejected, slammed the White House plan in a statement. He contended that the proposal puts Trump's "entire hardline immigration agenda — including massive cuts to legal immigration — on the backs of these young people."

Meanwhile, Congressional Hispanic Caucus Chair Michelle Lujan Grisham, D-N.M., said "Trump destroyed DACA, threatened Dreamers with detention and deportation, and is using that threat to enact his hardline immigration policies."

Trump had signaled on Wednesday that his proposal would include a path to citizenship for so-called Dreamers over 10 to 12 years. He told the hundreds of thousands of immigrants shielded from deportation and cleared to work under the Obama-era program "not to worry."