(CNN) Just hours after a bipartisan meeting on the future of hundreds of thousands of young immigrants, President Donald Trump tweeted that he still wanted to see a wall on the southern US border as part of any immigration deal.

What exactly the wall would look like and whether it was simply a rhetorical battle in the negotiations wasn't immediately clear. A senior White House official told CNN that a wall would have to be part of "phase one" of the immigration deal with Democrats.

As of Tuesday evening, a Democratic congressional aide said Democrats were still seeking more clarity from the White House, noting that there may be some wiggle room between a wall across the border and "border security."

"We don't have a lot of clarity on where they can land within that," the aide said.

But this aide cautioned if the White House is insisting on the wall, negotiations could fall apart.

"If he's still wedded to something ridiculous, then we can't," the Democratic aide said. "The details matter a lot."

Earlier in the day, after a meeting with Trump, key negotiators on an immigration bill in the Senate had said they were feeling more optimistic about the prospects for a fix to DACA, the Deferred Action for Childhood Arrivals program set to expire in March.

"I am actually more encouraged than ever. I think the President embraced a solution," said Sen. Lindsey Graham, a South Carolina Republican. "The one thing I did tell the President is there is no substitute for his involvement. He is the key person here. Congress needs his leadership and direction."

But more work remains. And as always, Trump's position could shift.

The meeting Tuesday was an unusually public one at the White House with Trump keeping the press in the room for nearly an hour as he meandered from a variety of topics from earmarks to immigration and proclaimed he was open to signing just about any DACA bill that the Congress sent him.

"I think my positions are going to be what the people in this room come up with," Trump said. "If they come to me with things I'm not in love with, I'm going to do it. Because I respect them."

Now the hard work comes as lawmakers in both parties in the House and Senate begin the next phase on Wednesday of filling in the details of a legislative package.

But already the two parties are not on the same page on what came out of the unusual televised negotiating session that featured the President assuring both Democrats and Republicans he backed their various positions.

For months, Republicans in Congress have been looking for explicit instructions from Trump on what he wants to see in a DACA bill, something that still appeared elusive at the end of the meeting Tuesday. Congressional negotiators, however, walked away with at the very least four items they would debate as part of any DACA deal. Republicans said Trump outlined he wanted to see changes to so-called "chain migration" -- or family-based migration, the diversity lottery system and bolstered border security.

"If we can stick with those limited topics, that's good news," said Sen. Jeff Flake, a Republican from Arizona who has been part of a key working group on DACA for the last several months.

But much distance remains between the broad contours of a deal and actually reaching one.

Rep. Steny Hoyer, the No. 2 House Democrat tasked with helping craft a package, released a statement saying the White House's take on the meeting was "inaccurate." He noted that while the GOP may say the plan would cover the four areas, as far as Democrats were concerned, "our priority remains the same: ensuring that (DACA recipients) can remain in the only country they've ever called home."

The deadline for DACA is March 5 and Democrats are pushing for a deal to be part of a January 19 spending deadline. Deep schisms within the GOP conference and long-simmering mistrust between Republicans and Democrats also threaten to derail any potential compromise.

Behind closed doors, a group of five lawmakers led by Republican Sen. Lindsey Graham of South Carolina and Sen. Dick Durbin of Illinois say they will continue working on their bill.

"The President and every member of Congress in that room agreed on the urgent need to fix this DACA crisis now. Republicans laid out their four priorities, and Democrats laid out ours: the Dream Act. The next step is for bipartisan negotiators, who have already been working for months, to immediately reach an agreement that can pass both chambers and be signed into law by January 19th," Durbin said in a released statement.

The group has been quietly hammering out a compromise for months and plan to meet again Wednesday, according to one Democratic aide.

If anything, Tuesday's meeting was viewed by many members of the Senate's working group as a stamp of approval for what they've poured months of negotiations into.

"Frankly, I went in with pretty low expectations. You don't put 22 people around the table and expect to really negotiate," Flake said on CNN. "We're at a point now where we really need to negotiate. I was surprised, when the cameras left, at the President's flexibility on the matter. And that he actually went in and explained what he meant by a wall and border security, and that's helpful. It really is."

Flake said Trump "drilled down a bit" on details surrounding such a border wall and the senator said what was described wouldn't be as long as it had been characterized during the presidential election.

"There won't be a 2,000-mile wall," Flake told CNN's Jake Tapper. "That we're looking at probably something (around) 7-800 miles."

Florida GOP Rep. Mario Diaz-Balart, who attended the White House session, said that many of the same members who attended Tuesday's meeting will also meet again Wednesday to try and find a way to merge their ideas together.

"These are intertwined," he said.

He believes that something will emerge soon from these talks, stressing "there is a sense of urgency. The President has a sense of urgency. All of us have a sense of urgency."

The Florida Republican, who noted that he's been involved in complicated immigration talks with three administrations, was optimistic that getting a deal on DACA and the other issues means there is hope for future action on the issue.

"If we do this, I think that pretty much shows that we can do other important things -- dealing with other issues dealing with immigration -- and I'm hoping with we could but we have to deal with this first for obvious reasons."