The White House has jumped into immigration negotiations on Capitol Hill, in an apparent bid to move the needle after Senate Minority Leader Chuck Schumer revoked his offer to help fund a U.S.-Mexico border wall.

With President Trump in Davos, Chief of Staff John Kelly plans to meet Thursday with lawmakers on Capitol Hill about a plan for 'Dreamers.'

But the prospect of another government shutdown looms large over talks, with the next deadline for a federal spending bill just two weeks away. The immigration issue led to the impasse that shuttered the government for three days over the weekend, and the heat Schumer is taking from the liberal base for backing down in that fight could serve to harden his resolve this time around.

“The clock is ticking,” Schumer admitted Wednesday, after saying a day earlier that his offer to Trump to provide billions for his U.S.-Mexico border wall in exchange for protecting tens of thousands of illegal immigrants is now “off the table.”

That drew a fiery response from Trump, who tweeted, “Cryin’ Chuck Schumer fully understands, especially after his humiliating defeat, that if there is no Wall, there is no DACA. We must have safety and security, together with a strong Military, for our great people!”

And it resulted in a counter threat from South Carolina GOP Sen. Lindsey Graham, who said: “If Senator Schumer takes something off the table, I’m sure we’ll take something off the table.”

At the center of the talks are two major issues – Trump’s push for billions to fund a border wall, and possible legislation to extend protections for illegal immigrants brought to the U.S. as children. Trump is ending the status they enjoyed under the Obama-era Deferred Action for Childhood Arrivals, or DACA, program, but is open to legislation.

'We're going to solve the problem.' — President Trump

To that end, Trump on Wednesday signaled he’s willing to give ground in that debate – and provide a pathway to citizenship for Dreamers.

"We're going to morph into it," Trump told reporters Wednesday. "It's going to happen, at some point in the future, over a period of 10 to 12 years."

Graham said in a statement that the president’s remarks represent “presidential leadership on immigration that will allow us to solve a difficult problem.”

Trump's pronouncements came as the White House announced it would unveil a legislative framework on immigration next week that it hopes can pass both the House and the Senate, dealing with DACA and border security and more.

The president's remarks amounted to a preview of that framework. He said he'll also propose $25 billion for building a wall on the U.S.-Mexico border and $5 billion for other security measures.

Despite his previously harsh rhetoric, Trump told reporters he had a message for the Dreamers: "Tell `em not to be concerned, OK? Tell `em not to worry. We're going to solve the problem."

Trump repeatedly has said that any deal to protect those immigrants from deportation is contingent on money for the border wall and other security measures. Trump also wants to limit the family members that immigrants are able to sponsor to join them in the U.S. and either replace or transform a visa lottery aimed at increasing diversity.

These complicated negotiations on issues that have vexed Washington for decades are playing out within an extraordinarily tight timetable, against a Feb. 8 deadline to pass a funding bill or face another shutdown.

The two-week deadline to reach an immigration deal was effectively set by Senate Majority Leader Mitch McConnell. The Kentucky Republican emerged amid the weekend shutdown to declare “it would be my intention to proceed to legislation that would address DACA,” in exchange for keeping the government open.

Schumer said Wednesday that such a fast-approaching deadline -- to reach an immigration deal before another shutdown -- should “light a fire under everybody.”

At least some members of the bipartisan group that brokered the weekend deal are now purportedly meeting to reach an agreement on immigration.

But even Illinois Sen. Dick Durbin, the No. 2 Senate Democrat behind Schumer, acknowledged Wednesday that Congress has no clear path forward.

“As of today, we don’t have a bill before us,” said Durbin. “We start anew.”

Durbin put the blame squarely on Trump, saying he “created the problem” last fall by ending DACA protections, effective March 5. However, he also faulted Congress for thus far failing to find a solution.

“Well here we are. We are just about at the fifth month in the sixth-month period that he gave us,” said Durbin, after Trump apparently rejected a bipartisan immigration-reform plan presented to him early last week.

Durbin also acknowledged that any deal reached in just two weeks would likely address only DACA and border security.

“It would be unrealistic to think we could address comprehensive reform in 14 days,” he said.

But Trump advisers purportedly urged the president to insist that any such deal also fix or end “chain migration” and a lottery-based immigration program, which critics say prioritizes diversity over a merit-based system for applicants. So-called chain migration essentially allows immigrants to bring their extended families into the U.S. with them.

Wisconsin GOP Sen. Ron Johnson said Wednesday that members of Congress are “probably further away than we’d like to be” on an immigration deal.

Many congressional Democrats and Republicans including House Speaker Paul Ryan want legislation to permanently protect Dreamers -- and perhaps achieve the elusive goal of improving the country’s flawed immigration system.

“We want to fix DACA. We want to fix DACA in a balanced way,” Ryan, R-Wis., said last week, while also making clear that such a deal would have to include border security.

But the possibility of passing a fix in the GOP-controlled House is also a challenge, considering its conservative wing has equated deportation protections for illegal immigrants with amnesty.

And ultimately, Trump, whom Democrats say has been difficult to pin down on immigration reform, will be a final decision-maker.

“I don’t know the position of the president of the United States now,” Durbin said. “I couldn’t express it after the experience we had a couple of weeks ago. … He hasn’t issued anything by way of a suggested piece of legislation. We haven’t heard from him.”

Fox News’ Peter Doocy and Jennifer Bowman and The Associated Press contributed to this report.