Undercutting the staff-level talks, Trump declared that only he could make a deal with Democratic leaders - "in 20 minutes, if they want to".
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Collins, one of at least three Senate Republicans who've called for reopening government while the debate over the wall continues, said she'd like to see Senate Majority Leader Mitch McConnell bring House-passed appropriation bills to the floor.
Trump said it would be easy to end the shutdown, calling for Democrats to negotiate.
Mick Mulvaney, Trump's acting chief of staff, told NBC's "Meet the Press" programme that agreeing to a steel separation would allow Democrats to stick to their refusal to fund a wall. On Saturday President Trump tweeted about the ongoing negotiations.
The new Democrat-led House passed legislation last week that would provide full-year money for eight of nine federal departments that have faced a funding lapse of more than two weeks, and extend current-year funding for the Department of Homeland Security through February 8.
President Donald Trump has stood firm on his demand for billions of dollars to fund a border wall with Mexico, claiming "tremendous" support inside his camp on the contentious issue which has forced a government shutdown now entering its third week.
The shutdown has left the Smithsonian museums, a major tourist draw, shuttered, garbage piling up at national parks, and workers concerned about paying their bills. Two Democratic officials familiar with the session say Democrats pleaded with Pence and other officials to re-open government while talks continue.
Adding to concerns, federal workers might miss this week's paychecks.
FILE - Director of the Office of Management and Budget Mick Mulvaney calls on a reporter during a White House briefing about a possible government shutdown, January 19, 2018, in Washington.
Trump, a former NY businessman, said he could relate to the workers who would have trouble paying bills because of the shutdown and threatened, again, to declare a national emergency as an alternative way to build the wall, depending on the outcome of talks in the coming days. It's been done a number of times but primarily it's been done to build facilities in Afghanistan and Iraq and in this case, I think the president would be wide open to a court challenge, saying 'where's the emergency?'" Smith told George Stephanopoulos on "This Week" on Sunday "You have to establish that in order to do this. "It is too early to talk about that intelligently", Nadler, whose committee would oversee any impeachment effort, said on CNN on Friday morning. Previously, the president had tweeted he didn't care that "most of the workers not getting paid are Democrats". Some areas will be all concrete but the experts at Border Patrol prefer a Wall that is see through (thereby making it possible to see what is happening on both sides).
"I can relate, and I'm sure the people who are on the receiving end will make adjustments; they always do", Trump said.
"That should help us move in the right direction", he said. His administration has already spent millions constructing wall prototypes near the border in San Diego.