“I’ll take all the heat you want,” Trump told nearly two dozen lawmakers on Tuesday at the White House for a meeting that began with a startling 55 minutes in which reporters and TV cameras watched.

“But you are not that far away from comprehensive immigration reform.”

Trump said an immigration deal could be reached in two phases – first by addressing young immigrants and border security with what he called a “bill of love,” then by making comprehensive changes that have long eluded Congress.

That second bill would likely face long odds for passage, considering long-running disagreements over issues like how to handle all 11 million illegal immigrants that are currently in the US.

Republicans will need Democratic votes to prevent a federal shutdown in 10 days – votes Democrats have threatened to withhold without an immigration agreement.

House Majority Leader Kevin McCarthy of California told reporters on Tuesday that talks would begin as early as Wednesday, vowing that they would “solve this problem and find common ground.”

Negotiations over the Deferred Action for Childhood Arrivals (DACA) programme, which protects people brought into the US illegally as children, may be more complicated after Trump’s attempt to repeal it was temporarily blocked by a judge on Tuesday night.

Thw Obama-era DACA programme has given hundreds of thousands – the so-called Dreamers – a shield from deportation and the right to work legally.

Trump ended it last year, but gave Congress until March 5 to find a fix, and Tuesday he signalled flexibility. “I think my positions are going to be what the people in this room come up with,” he said during the Cabinet Room meeting.

In blocking that move, US District Judge William Alsup in San Francisco granted a request by California and other plaintiffs to let lawsuits over the administration’s decision play out in court.

Alsup said lawyers in favour of DACA clearly showed that the young immigrants “were likely to suffer serious, irreparable harm” without court action. The judge also said the lawyers had a strong chance of succeeding at trial.

Early Wednesday, White House press secretary Sarah Huckabee Sanders said the ruling was “outrageous, especially in light of the President’s successful bipartisan meeting with House and Senate members at the White House on the same day.”

She said the issue should “go through the normal legislative process” and pledged Trump “will work with members of both parties to reach a permanent solution.”

Trump, meanwhile, has slammed the move on Twitter as “unfair,” despite his apparent willingness to discuss terms on Tuesday.

After Trump and lawmakers spent time meeting privately on Tuesday, the White House and numerous lawmakers said there was agreement to limit the immediate bill to four areas.

These were border security, family-based “chain migration,” a visa lottery that draws people from diverse countries and how to revive DACA.

In another rare show of conciliation, Trump even flashed some give on his cherished plan to build a wall along the border with Mexico, perhaps his highest profiled pledge from last year’s presidential campaign.

That proposal has been strongly opposed by Democrats and many Republicans as a futile waste of money.

Trump said it need not be a “2,000-mile wall. We don’t need a wall where you have rivers and mountains and everything else protecting it. But we do need a wall for a fairly good portion.”

He had made similar statements last year, but this time it was in the context of negotiations for actual legislation.

Both parties were already showing signs of divisions over how much to give in upcoming talks. But one conservative foe of giving ground acknowledged the impact of Trump’s support.

“There are scores of Republicans who have shifted their position to follow the president,” said Republican representative Steve King of Iowa.

He said that while he helped head off a bipartisan immigration effort in 2013, “I don’t want to promise the result will be the same. This is more momentum than I have ever seen.”

Among Democrats, representative Henry Cuellar of Texas, who attended the White House meeting, said he was open to negotiations on the four issues bargainers will address.

One attendee, No 2 Senate Democratic leader Dick Durbin of Illinois, said: “The sense of urgency, the commitment to DACA, the fact that the president said to me privately as well as publicly, ‘I want to get this done,’ I’m going to take him at his word.”

Underscoring the effort’s fresh momentum, the head of the Congressional Hispanic Caucus, Democratic representative Michelle Grisham Lujan of New Mexico, said late on Tuesday she was “encouraged” by Trump’s words and would work “in good faith” toward a deal. Some of the group’s members have taken a hard line against surrendering too much in a compromise with Trump.

Conservatives quickly sounded alarms about a process that would lead to a comprehensive agreement on immigration, a path that has long been anathema to many rank-and-file Republicans.

Republican representative Mark Meadows of North Carolina, leader of the hard-right House Freedom Caucus, said in a text message after the White House meeting he was “generally” opposed to a two-step process “because history would indicate the second step never happens.”

He later said that if the first steps included the four areas outlined by the White House, “then I could support a two-step process realising that step one is the only thing that is guaranteed.”