"It's gonna happen at some point in the future, over a period of 10-12 years", Trump said.
The plan will propose border security measures, closing loopholes, ending so-called chain migration, canceling the visa lottery program and legalizing the Deferred Action for Childhood Arrivals, or DACA, program, she added.
The Senate is slated to vote today at noon to proceed on a proposal that will fund the government through February 8.
The White House will release a "legislative framework" for an immigration deal on Monday that it believes can earn bipartisan support, White House press secretary Sarah Sanders said. Trump also wants to limit the family members that immigrants are able to sponsor to join them in the US and either replace or transform a visa lottery aimed at increasing diversity.
"Cryin' Chuck Schumer fully understands, especially after his humiliating defeat, that if there is no Wall, there is no DACA", Trump tweeted shortly before midnight Tuesday.
"What the president did clearly worked", Sanders responded with unearned smugness, noting that Trump's disengagement allowed the crisis to be solved by Schumer.
USA official urges Turkey to halt Syria campaign
But Turkey considers the YPG as part of the long Kurdish insurgency for an independent Kurdistan which would include part of Turkey.
South Carolina's Sen. Lindsey Graham, a key Republican negotiator, called the White House's plan to release a framework "excellent", noting the importance of getting the White House's "input".
After the meeting, Democratic Senator Claire McCaskill expressed cautious optimism to reporters about Trump's framework, saying "that could go either way", when asked if it will be helpful to lawmakers.
"I think an terrible lot of the certain members of Congress used this as perpetual excuse: 'We don't know where the president is at, '" a senior administration official said.
It is unclear whether several of Trump's priorities in October are part of the current negotiations, including the introduction of mandatory e-verify, which proponents say is critical to stopping the continual flow of illegal immigrants.
The Kentucky shooting and Sanders' response came more than three months after Sanders and the President promised the White House would eventually engage in a "policy discussion" and discuss "gun laws" in the wake of the Las Vegas mass shooting. The press secretary said the White House wanted to see a "swift conclusion" to the investigation and criticized the media "obsession" over the minute developments of the Mueller investigation.
The Senate's top Democrat, Chuck Schumer, is pulling back an offer of $25 billion for President Donald Trump's southern border wall.
Trump's chief of staff, John Kelly, was slated to meet with lawmakers on Capitol Hill on Thursday, a senior White House official said. Both senators are the deputy leaders of their respective parties and sit on a Senate Judiciary Committee subcommittee on immigration policy.