Speaking to "Fox News Sunday," White House Press Secretary Sarah Sanders affirmed that President Trump remains willing to declare a "national emergency" to ensure that his proposed southern border wall is constructed -- even if, as they have vowed, Democrats in Congress refuse to fund it.

Sanders also revealed that while "some progress" was made during Saturday's negotiations between top Democrats and White House officials and House Democrats over how to end the ongoing partial federal government shutdown over wall funding, Democrats didn't appear willing to reach a deal.

"Democrats set down -- the first thing that one of the individuals from the Democrats’ side said in the meeting was, 'We’re not here to make an agreement.' So this is the beginning of a conversation that still has, I think, a lot left to be worked out. They’re going to meet again later this afternoon, and hopefully they’ll continue to make progress and continue to move the ball down the field."

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Pressed by Chris Wallace as to whether the government shutdown could indeed last for more than a year, as President Trump warned last week, Sanders didn't hesitate.

"Absolutely -- the president means what he says when he says that," Sanders said, adding that it was "outrageous" and "incomprehensible" for Democrats who have said they favor border security to oppose his border wall.

When the new Congress took office on Thursday, Democrats quickly passed two spending bills that would have funded the Department of Homeland Security and fully reopened several other agencies -- but none of the bills included any border wall funding, and Senate Republicans and the White House called them nonstarters.

Sanders denied that the White House was holding underfunded departments like Treasury "hostage" to gain "leverage," saying instead that Trump "wants to do this all at once. He knows it’s better if they can focus on getting all of these packages done at one time."

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After Sanders remarked that "nearly 4,000 known or suspected terrorists come into our country illegally, and we know that our most vulnerable point of entry is at our southern border," Wallace interjected, noting that the overwhelming majority of those individuals are captured at airports -- not at the border -- and that the State Department has said there is no credible evidence of a terrorist coming across the southern border.

"Not always," Sanders said. "But certainly a large number [are apprehended at airports]. It's by air, it's by land, and it's by sea. It's all of the above. ... The most vulnerable point of entry that we have into this country is the southern border."

Wallace additionally challenged Sanders on the Trump administration's claims that many "special interest aliens" have been stopped at the border. So-called special interest aliens, Wallace pointedly reminded Sanders, are those that come from countries known to produce terrorists, but are not necessarily terrorists themselves.

The White House press secretary also doubled down on Trump's comments during an impromptu Rose Garden press conference on Friday, when he told reporters, “We can call a national emergency [to build a border wall] because of the security of our country. ... “I may do it. I may do it. ... If we can do it through a negotiated process, we’re giving it a shot.”

"The president’s prepared to do what it takes to protect our borders, to protect the people of this country," Sanders told host Chris Wallace. "He knows that the No. 1 job he has as president and commander-in-chief is to protect its citizens."

The Friday press conference underscored how far apart both sides are, even as Trump called the meeting "productive" and suggested the standoff could end soon -- or not. He indicated he was not shifting on his demand for more than $5 billion for funding for a wall on the southern border, saying it was necessary as the border is a "dangerous, horrible disaster."

"This is national security we’re talking about, we’re not talking about games," he told reporters. “We're not playing games, we have to do it."

Speaking separately to Wallace on "Fox News Sunday," Democratic Rhode Island Rep. David Cicilline suggested Trump does 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."

Cicilline also demanded that the government re-open "immediately" and declined to condemn Michigan Democratic Rep. Rashida Tlaib for calling Trump a "motherf---er" and vowing to impeach him last week. It was hypocrtical for Republicans to "clutch their pearls" over the issue, Cicilline said, given Trump's previous remarks.

Meanwhile, in an interview broadcast Sunday on NBC's "Meet the Press," Acting White House Chief of Staff Mick Mulvaney told host Chuck Todd that Trump "was willing to agree, and he mentioned this at the Rose Garden press conference, to take a concrete wall off the table."

Mulvaney had met with senior congressional officials on Saturday to try to make progress on a compromise, although he suggested the encounter had been mostly unproductive. Trump was scheduled to discuss border security Sunday at Camp David.

"If that is not evidence of our willingness to solve the problem," Mulvaney said. "Because again, what's driving this is the president's desire to change the conditions at the border. And if he has to give up a concrete wall, replace it with a steel fence in order to do that so that Democrats can say, 'See? He's not building a wall anymore' that should help us move in the right direction."