Trump is demanding over 5 billion US dollars in border security to deliver his signature campaign promise to build the border wall, whose construction and funding have been strongly rejected by Democrats.
A White House official told CNN on Saturday that Trump was leaning towards declaring a national emergency to use military funding for his wall. Perhaps that could have been on a massive infrastructure initiative that would permit Mr. Trump to address his campaign concerns over the disrepair of American bridges, roads and airports even as it would allow Ms. Pelosi and Mr. Schumer to extend a hand to the Democrats' traditional big-labour allies, many of whom drifted into the Trump camp in the 2016 election.
"This shutdown could end tomorrow and it could also go on for a long time", Trump said.
A migrant from Honduras pass a child to her father after he jumped the border fence to get into the US side to San Diego, Calif., from Tijuana, Mexico.
Sunday is the 16th day of the ongoing partial government shutdown, which has affected nine cabinet-level departments and dozens of agencies as well as the jobs and paychecks of some 800,000 federal employees.
Acting White House chief of staff Mick Mulvaney said in a separate interview on the same program that talks on Saturday to reopen the government "did not make much progress". He said Trump was willing to forgo a concrete wall for steel or other materials.
Showing little empathy for the hundreds of thousands of federal workers furloughed or working without pay, Trump declared - without citing evidence - that most are Democrats.
"Democrats and now a growing number of Republicans are coming together and saying let's open up the government and debate border security separately", Schumer told reporters in NY.
Democrats could demand other concessions from the White House, such as protections for immigrants brought illegally to the United States as children, known as Dreamers, or changes to other spending provisions.More news: CHINA - USA Huawei employees punished for tweeting with Iphone
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She added, "I think, you know, President Trump has met his match".
"Look, if Harry Truman couldn't nationalize the steel industry during wartime, this President doesn't have the power to declare an emergency and build a multibillion dollar wall on the border", Schiff said.
With his negotiators preparing for the afternoon session, Trump said he didn't expect it to produce a resolution.
However, Senate Majority Leader Mitch McConnell said last week he would not put any legislation to a vote in the Senate unless Trump supported it.
The $5.6 billion he wants for a border wall is at the center of the partial government shutdown which is stretching into the third week.
However, such a move could face legal challenges in court.
The president has already suggested his definition of the wall is flexible, referring to slats and other "border things".
Sarah Huckabee Sanders tells "Fox News Sunday" that the White House has been looking at "every option available" to get the needed money, and she says Trump will do "whatever it takes to protect our borders".
"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?" Mexico has refused. He's now demanding the money from Congress.