A bipartisan group of senators says they have clinched a deal to provide protections to young immigrants known as Dreamers, but are facing pushback from President Trump Donald John TrumpObama calls on Senate not to fill Ginsburg's vacancy until after election Planned Parenthood: 'The fate of our rights' depends on Ginsburg replacement Progressive group to spend M in ad campaign on Supreme Court vacancy MORE and GOP leadership.

Sens. Jeff Flake Jeffrey (Jeff) Lane FlakeRepublican former Michigan governor says he's voting for Biden Maybe they just don't like cowboys: The president is successful, some just don't like his style Bush endorsing Biden? Don't hold your breath MORE (R-Ariz.) and Dick Durbin Richard (Dick) Joseph DurbinMcConnell focuses on confirming judicial nominees with COVID-19 talks stalled Senate Republicans signal openness to working with Biden Top GOP senator calls for Biden to release list of possible Supreme Court picks MORE (D-Ill.) said Thursday the group of six senators has locked down an agreement amongst themselves on pairing a fix for the Deferred Action for Childhood Arrivals (DACA) program with a border security package.

"We've got this bipartisan group. We are at a deal. ... It's the only game in town," Flake told reporters.

But Durbin and Sen. Lindsey Graham Lindsey Olin GrahamSenate Republicans face tough decision on replacing Ginsburg Democratic senator calls for eliminating filibuster, expanding Supreme Court if GOP fills vacancy What Senate Republicans have said about election-year Supreme Court vacancies MORE (R-S.C.) were told during a Thursday meeting with President Trump at the White House that he was not ready to sign on to the bill.

"We were hoping for that, but the president is not prepared to do that at this moment," Durbin said when asked if they wanted the president's support before they moved forward with their agreement.

Press secretary Sarah Huckabee Sanders, during a press briefing, said, "There has not been a deal reached yet. However, we still think we can get there and we are very focused on trying to make sure that happens."

The group of senators holding the talks — which also includes Democratic Sens. Michael Bennet Michael Farrand BennetOVERNIGHT ENERGY: House Democrats tee up vote on climate-focused energy bill next week | EPA reappoints controversial leader to air quality advisory committee | Coronavirus creates delay in Pentagon research for alternative to 'forever chemicals' Senate Democrats demand White House fire controversial head of public lands agency Next crisis, keep people working and give them raises MORE (Colo.) and Bob Menendez (N.J.) and Republican Sen. Cory Gardner Cory Scott GardnerSenate Republicans face tough decision on replacing Ginsburg What Senate Republicans have said about election-year Supreme Court vacancies Chamber of Commerce endorses McSally for reelection MORE (Colo.) — has been negotiating for months on a deal that would include a fix for DACA.

Their bill is expected to include legalization for DACA recipients, known as Dreamers, as well as a border security package and changes to the State Department's diversity visa lottery program and family-based immigration policies.

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Those four parameters are in line with what Trump and lawmakers agreed to during a White House meeting earlier this week.

The six senators said in a joint statement Thursday afternoon they have reached an agreement, which would include a path to citizenship.

"President Trump called on Congress to solve the DACA challenge. ... We are now working to build support for that deal in Congress," they said.

Durbin said the bill would include a pathway to citizenship not only for current DACA recipients, but other immigrants in the country illegally who would qualify for the program.

Meanwhile, Flake indicated that any changes to family-based immigration would be narrowly focused to the current DACA population and their family members, and not apply, as some Republicans want, to the entire immigration population.

Flake also said senators had discussed reallocating some of the State Department's diversity lottery visas to people who have Temporary Protected Status (TPS), a program the Trump administration has been scaling back.

Both Flake and Durbin have declined to discuss specific border security numbers. But Durbin indicated Wednesday night that the border security package would include funding for fencing and barriers, but also technology.

Durbin confirmed that he believed the group has an agreement and they are "working to get support from the other senators, on both sides of the aisle, and we won't be releasing draft or final version at least through the weekend."

Flake added that members of the working group will try to line up more co-sponsors before releasing details of their deal.

"We're shopping it among our colleagues," he said. "We got a few others already said they'll sign on and we're working on others before we release details of it."

Staffers for Durbin, Sen. John Cornyn John CornynBipartisan praise pours in after Ginsburg's death Chamber of Commerce endorses McSally for reelection Airline job cuts loom in battleground states MORE (R-Texas) and Reps. Steny Hoyer Steny Hamilton HoyerHouse Democrats postpone vote on marijuana decriminalization bill Democrats scramble on COVID-19 relief amid division, Trump surprise The Hill's Morning Report - Sponsored by The Air Line Pilots Association - Pence lauds Harris as 'experienced debater'; Trump, Biden diverge over debate prep MORE (D-Md.) and Kevin McCarthy Kevin Owen McCarthyTrump asked Chamber of Commerce to reconsider Democratic endorsements: report The Hill's Morning Report - Sponsored by The Air Line Pilots Association - White House moves closer to Pelosi on virus relief bill Trump's sharp words put CDC director on hot seat MORE (R-Calif.) are expected to meet Thursday as part of separate discussions to figure out a path forward.

"Kevin McCarthy asked for a chance to move forward. ... We'll work with him to see what we can achieve," Durbin said.

Still, the White House suggested the emerging Senate agreement was not something Trump would accept, even though the president on Tuesday suggested he would sign whatever immigration bill lawmakers sent to his desk.

Marc Short, the White House director of legislative affairs, said the president has not signed on to the agreement and that there is a "long ways to go."

He added that the White House is "not looking for DACA to be the DREAM Act" — referring to the Development, Relief and Education for Alien Minors (DREAM) Act that provides a path to citizenship.

Short added the president wants changes to "chain migration" to go broader than just impacting the DACA population, a potential hurdle from the bipartisan Senate group's deal.

"I think we're pleased that bipartisan members are talking ... but I still think there's a ways to go," he said.

GOP Sens. Tom Cotton Tom Bryant CottonRenewed focus on Trump's Supreme Court list after Ginsburg's death Republicans call for DOJ to prosecute Netflix executives for releasing 'Cuties' Loeffler calls for hearing in wake of Netflix's 'Cuties' MORE (Ark.) and David Perdue (Ga.), McCarthy and Rep. Bob Goodlatte Robert (Bob) William GoodlatteNo documents? Hoping for legalization? Be wary of Joe Biden Press: Trump's final presidential pardon: himself USCIS chief Cuccinelli blames Paul Ryan for immigration inaction MORE (R-Va.) — who have not been part of the bipartisan Senate talks — were also part of Thursday's White House meeting.

Cornyn said a message had been delivered that the bipartisan group would not be able to single-handedly decide what the final DACA agreement is.

"I think what the president told them is its fine for them to negotiate ... but what they need to do is share that with others so it will have broad enough support to actually get passed," he said.

The Trump administration announced last year that they were ending the DACA program, giving Congress a March deadline to codify the Obama-era program into law.

Both sides have appeared sympathetic to DACA recipients, but Congress has struggled to come up with a broad agreement that could win enough support to overcome likely pushback from conservatives as well as progressive Democrats.

Goodlatte was part of a group of House Republicans who introduced their own proposal this week, but that bill is unlikely to be able to win over enough support to pass the Senate.

- Alex Bolton contributed

Updated at 4:24 p.m.