US President Donald Trump has said he is "fairly close" to a bipartisan deal to protect young undocumented migrants known as Dreamers.
Mr Trump told journalists at the White House that any agreement must include "massive border security".
The president said funding for his proposed border wall on the US border with Mexico was not part of the pact.
Mr Trump spoke a day after talks with top Democrats Nancy Pelosi and Chuck Schumer at the White House.
The president's right-wing supporters are infuriated.
Only last week Mr Trump stunned fellow Republicans by making a budget deal with the Democrats.
Does anybody really want to throw out good, educated and accomplished young people who have jobs, some serving in the military? Really!.....— Donald J. Trump (@realDonaldTrump) September 14, 2017
...They have been in our country for many years through no fault of their own - brought in by parents at young age. Plus BIG border security— Donald J. Trump (@realDonaldTrump) September 14, 2017
The Deferred Action for Childhood Arrivals (Daca) programme allows some 800,000 people to remain in the US, and provides temporary permits for work and study.
The Obama-era scheme was put in place to protect so-called "Dreamers" - migrants who entered the US illegally as children - from deportation.
Only last week Mr Trump announced he would cancel the programme.
He said he was giving Congress six months to enact a replacement plan for Daca recipients.
Deal or No Deal - Anthony Zurcher, BBC News Washington
Welcome to another episode of Deal or No Deal, White House edition. Unlike the classic game show, however, Donald Trump appears to be playing against himself.
In a series of tweets, the president denied he had struck an immigration/border security agreement with Democratic congressional leaders, then effectively endorsed the same terms they set out in a press release Wednesday night.
When speaking to reporters, he even echoed Democratic justifications for why undocumented immigrants who entered the US as children should be given normalised residency status.
This comes as a shock to some of Trump's diehard anti-immigration supporters, who view any Daca-like agreement as amnesty for law-breakers. Congressional Republicans, who were working on their own deal with Democrats, are in a daze as well.
There is the possibility that this could be a Nixon-in-China moment for the president, where only a man who campaigned vociferously against undocumented immigrants could agree to give legal residency to hundreds of thousands of them.
Unlike Nixon's China diplomacy, however, Mr Trump will need congressional Republicans to go along with his deal. Many voted against his earlier agreement to raise the debt limit and avoid a government shutdown.
This could be an even heavier lift.
Heading to Florida on Thursday morning to view the damage from Hurricane Irma, Mr Trump told journalists: "We're working on a plan subject to getting massive border control, we are working on a plan for Daca. People want to see that happen."
He added: "So we met last night with, as you know, with Schumer, Pelosi and a whole group and I think we're fairly close but we have to get massive border security."
The president said the congressional Republican leadership was "on board" with the plan.
"The wall is going to be built," he added. "It will be funded a little bit later."
Democrats have repeatedly vowed to block any legislation that includes funding for the border wall - a key campaign pledge by Mr Trump.
After arriving in Florida, Mr Trump denied that he would back a path to citizenship for Dreamers.
"We're not looking at amnesty," he said.
During the presidential campaign, in August 2015, Mr Trump said in a TV interview that Dreamers "have to go".
But on Thursday, he voiced support for the young immigrants in language that echoed former President Barack Obama.
"Does anybody really want to throw out good, educated and accomplished young people who have jobs, some serving in the military? Really!" Mr Trump tweeted.
Paul Ryan, the top Republican in Congress, said Mr Trump's meeting with Democrats "was a discussion not an agreement or a negotiation".
Ms Pelosi told reporters no deal had been finalised with the president.
But she added: "We had an agreement to move forward in our view, with a Dream Act as the basis for how we protect the Dreamers, and for further discussions on what provisions relating to the border might be and an accompanying bill or whatever as we go forward."
Democrats failed to get Daca on to the statute books during the Obama administration, so it would be a political coup to succeed in doing so when Republicans control the White House and Congress.
Mr Trump's ultraconservative supporters are now upset.
Congressman Steve King of Iowa tweeted at the president that, if the latest reports are true, "Trump base is blown up, destroyed, irreparable, and disillusioned beyond repair. No promise is credible."
One of Mr Trump's earliest backers, media commentator Ann Coulter, tweeted: "At this point, who DOESN'T want Trump impeached?"
Breitbart, the website run by Mr Trump's former chief strategist Steve Bannon, ran the headline, "Amnesty Don" and accused the president of "a full-fledged cave".
What is Daca?
The Deferred Action for Childhood Arrivals (Daca) programme was created in 2012 by then-President Barack Obama to shield children of undocumented immigrants from deportation.
It also provided work and study permits for those it covered - popularly known as "Dreamers".
In order to qualify for Daca, applicants under the age of 30 were required to submit personal information to the Department of Homeland Security, including addresses and phone numbers.
They had to pass an FBI background check, have a clean criminal background, and either be in school, recently graduated or have been honourably discharged from the military.
In exchange, the US government agreed to "defer" any action on their immigration status for a period of two years.
The majority of Dreamers are from Mexico and other Latin American countries.
The Department of Justice has said no new Daca applications will be taken.