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After President Trump and Vice President Mike Pence wrapped up separate meetings on border security and the ongoing partial federal government shutdown on Sunday, Trump offered his strongest endorsement yet of a proposal to build a steel wall, rather than a concrete barrier, at the southern border.

Meanwhile, a Democratic source told Fox News that the Pence-led meeting with bipartisan congressional staff at the Eisenhower Executive Office Building (EEOB) near the White House had accomplished little, and started nearly an hour late because Trump administration officials were unprepared. Trump called the meeting "productive" afterward, although he was not in attendance.

The president framed his new pitch for a steel wall as a concession to Democrats to move negotiations along, as the shutdown entered its 16th day. Meanwhile, Democrats published the full text of several spending bills to reopen the government on Sunday that the White House and Senate Republicans have long said have no chance of becoming law because they do not include any funding for a wall of any kind.

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"They don't like concrete, so we'll give them steel," Trump told reporters after returning to the White House from a meeting with his advisers at Camp David.

Trump also suggested he would rather wait until the Supreme Court rules on the legality of his administration's recission of the Obama-era Deferred Action for Childhood Arrivals (DACA) program before negotiating with Democrats on the issue as part of the talks to end the shutdown.

Several federal judges have held that the Trump administration's reasons for terminating DACA were legally insufficient under a federal administrative law statute, which requires adequate notice and justification before the government terminates a right it has previously granted.

"I would consider DACA, but ... I'd rather have the Supreme Court rule, and then work with the Democrats on DACA,' Trump said. "I want to help with DACA, but ... you know, it's going to be before the Supreme Court very soon."

At the sit-down at the EEOB, Pence -- along with Trump adviser and son-in-law Jared Kushner and Homeland Security Secretary Kirstjen Nielsen -- on Sunday discussed a variety of border-security measures with congressional officials from both parties.

“Democrats were given what they asked for, which was a detailed, breakdown list of the administration’s proposals for border security that include the wall and other border protection measures," a House GOP leadership aide told Fox News. "Democrats were given the opportunity to ask questions of Secretary Nielsen and hear DHS’ justification for the specific funding requests. Their justifications made it abundantly clear why it is necessary to have this level of funding to effectively secure our border.”

A Democratic official familiar with the meeting, however, said "no progress was made" at the Pence sit-down and charged that the White House was unprepared.

Vice President Mike Pence, left, White House legislative affairs aide Ja'Ron Smith, Homeland Security Secretary Kirstjen Nielsen, second row left, White House Senior Adviser Jared Kushner, and others, walk down the steps of the Eisenhower Executive Office building, on the White House complex, after a meeting with staff members of House and Senate leadership, Saturday, Jan. 5, 2019, in Washington. (AP Photo/Alex Brandon)

“The meeting today at 1 p.m. started approximately 45 minutes late because the White House did not have the information Democrats requested ready," the official told Fox News. "Yesterday, Democrats asked for a full budget justification for the administration’s position because the $5.7 billion wall request was not included in the administration's fiscal year 2019 request and the administration has not had a consistent position in various conversations with the Hill.  Democratic staff did not receive a full budget justification today."

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The Democratic source continued: "Three and a half months into a new fiscal year, the Administration did not present any commensurate cuts in the DHS budget to accommodate the increases they are seeking.  Given the failure of the White House to present a full budget justification today, the Democratic staff pleaded again for the White House to change course and re-open government by supporting the [bill to fund DHS through February 8] and the six bill package that the House has passed and has received broad bipartisan support in the Senate.  The Vice President said the President would not do that."

No further meetings between Pence and congressional staff are currently planned. For his part, Pence tweeted only that he was "back at the White House" Sunday afternoon.

While Pence noted that the president was "committed to securing the border, building the wall, & working to reopen our government," he did not characterize the meeting "productive," as he did on Twitter after a similar get-together with congressional staff on Saturday.

However, in his own tweet later Sunday afternoon, Trump called Pence's meeting as a step forward.

"V.P. Mike Pence and group had a productive meeting with the Schumer/Pelosi representatives today," Trump wrote. "Many details of Border Security were discussed. We are now planning a Steel Barrier rather than concrete. It is both stronger & less obtrusive. Good solution, and made in the U.S.A."

Trump's steel wall proposal was the continuation of a White House strategy that has developed in the past several weeks. Trump first floated the idea of using "artistically designed steel slats" for the wall, rather than concrete, in December.

He then suggested taking the concrete wall off the table at a Rose Garden news conference on Friday, as a concession to Democrats. And, acting White House chief of staff Mick Mulvaney said in an interview on NBC News' "Meet the Press" on Sunday that Trump "was willing to agree ... to take a concrete wall off the table" in order to secure a deal to end the ongoing shutdown.

"We've been in touch with a lot of people, and I informed my folks to say that we'll build a steel barrier --- steel -- that it will be made out of steel, that it will be less obtrusive and it'll be stronger," Trump said. "And we're able to use our great companies to make it, by using steel."

Some ex-White House officials have suggested Trump abandoned the idea of a concrete wall in the early days of his tenure. In an explosive interview published shortly before his departure from the Trump administration at the end of last year, former chief of staff John Kelly told the Los Angeles Times that the White House had "left a solid concrete wall early on in the administration, when we asked people what they needed and where they needed it."

People look on from the Mexican side, left, as U.S. Border Patrol agents on the other side of the U.S. border wall in San Diego prepare for the arrival of hundreds of pro-migration protestors, seen from Tijuana, Mexico, Monday, Dec. 10, 2018. (AP Photo/Rebecca Blackwell)

Earlier Sunday, speaking to reporters before he headed out to Camp David to discuss border security with top advisers, Trump had predicted that the Pence-run meeting would not lead to any major developments.

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"I don't expect to have anything to happen at that meeting," Trump said.

Previous meetings between Democrats and White House officials have been heated: House Speaker Nancy Pelosi and Nielsen, the DHS secretary, reportedly got into a tense confrontation on Wednesday in the Situation Room, with the California Democrat interrupting Nielsen’s presentation on border security and illegal immigration, telling her, “I reject your facts.”

The president additionally said he was "totally involved" in shutdown negotiations and claimed to have "tremendous support within the Republican Party."

The longest federal government shutdown in U.S. history lasted 21 days, and Trump has said repeatedly that current one may last more than a year if Democrats are not willing to fund some of the wall.

."They don't like concrete, so we'll give them steel."

— President Trump

The president also reaffirmed that he "may declare a national emergency dependent on what's going to happen over the next few days" to construct a border wall, and declared that Republicans and Democrats were "going to have some very serious talks" beginning on Monday.

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However, speaking on "Fox News Sunday," Democratic Rhode Island Rep. David Cicilline suggested Trump did not have the authority to declare an emergency to build the border wall.

"I don’t think the president has that authority -- he would have to meet a very high standard," Cicilline said. "Article I establishes the Congress of the United States and gives us the responsibility of appropriating money, so I don’t think the president has the authority to do that, and I hope he will try to work with Congress to resolve this disagreement but open the government first."

The Democrat-led House last week approved one amalgamated spending bill, addressing six areas of spending and one measure to fund the Department of Homeland Security through Feb. 8. The House approved both bills on a bipartisan basis, but Senate Republicans and the White House have said they were non-starters without wall money.

A migrant from Honduras pass a child to her father after he jumped the border fence to get into the U.S. side to San Diego, Calif., from Tijuana, Mexico, Thursday, Jan. 3, 2019. Discouraged by the long wait to apply for asylum through official ports of entry, many migrants from recent caravans are choosing to cross the U.S. border wall and hand themselves in to border patrol agents. (AP Photo/Daniel Ochoa de Olza)

This week, the House is set to start approving these measures on an individual basis. On Sunday, Democrats posted the full text of the bills, in keeping with their recent rules change requiring 72 hours of advanced notice to the public before members vote on most new legislation.

Fox News has learned the House Rules Committee will meet late Tuesday afternoon to tee up some of these measures for the floor. The Rules Committee is the gateway for most legislation to reach the House floor.

The House is expected to consider the Financial Services and General Government appropriations bill Wednesday. This measure deals with the Treasury Department and funds the Internal Revenue Service (IRS).

By the end of next week, the House likely will have passed different versions of all funding bills to re-open the government -- twice.

In an interview Sunday, South Carolina Republican Sen. Lindsey Graham warned the shutdown could not end as long as the "radical left" insisted on calling Republicans racist for supporting immigration officials.

"We’re negotiating with people who will accuse all of us who support a wall as part of border security as racists," Graham said on CBS News' "Face the Nation" on Sunday. "As long as the radical left is in charge, we’re not going to get anywhere."

Fox News' Chad Pergram and Chris Wallace contributed to this report.