Mr Trump fired off a series of tweets pushing back against the notion that he does not have a strategy to end what became the longest government shutdown in U.S. history when it entered its 22nd day on Saturday.
"Democrats should come back to Washington and work to end the Shutdown, while at the same time ending the frightful humanitarian crisis at our Southern Border", Mr. Trump tweeted.
"The easy solution is for me to call a national emergency".
"Sarah St. Vincent, a surveillance researcher at Human Rights Watch, wrote on Twitter that "'more surveillance' has become the default answer to far too many hard policy questions".
Trump contended, "I'm ready, willing and able to get a deal done...."
But Republican congressman Mark Meadows, who is close to the president, said that option was not under serious consideration.
Trump on Saturday said that the Democrats could "solve the Shutdown in 15 minutes".
He says Democrats don't support a wall costing billions of dollars that will, in his words, "destroy sensitive lands, take private property, and can be tunneled under, climbed over or cut through".
In Detroit, federal worker Gregory Simpkins told the Associated Press news agency, "Next week, it's going to be a panic mode".
Trump reiterated his argument that crime, illegal drugs, and human trafficking are creating a national security and humanitarian crisis at the border, and that a wall is needed.More news: Marvel's The Punisher Season 2 Trailer Shows Billy Russo Amassing an Army
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An effort by GOP senators led by Graham for a compromise deal that provided both border wall funding as well as immigration provisions appealing to Democrats stalled on Thursday as the President was not in favor, according to two people directly involved.
U.S. media report the White House is considering diverting some of the $13.9bn allocated a year ago by Congress for disaster relief in such areas as Puerto Rico, Texas and California to pay for the wall.
An emergency declaration by Mr Trump could break the stalemate by letting him use existing, unspent money to build the US-Mexico border wall, without needing congressional approval.
Trump has said he prefers giving Congress more time to work out a deal before pulling the trigger on such a declaration.
But Republicans who control the Senate have so far stood with Trump and insisted that any spending bills include money for his wall. Increasingly, Trump's only exit - and perhaps even his preferred choice - appears to be declaring an emergency, an act some in his own party oppose.
"If the president was a private citizen, if he was back at the Trump Corporation, he'd be looking at what's going on in Washington and scratching his head".
Trump spoke during a discussion with state, local and community leaders about border security and safe communities. He has even threatened to cut off federal emergency funds for fighting wildfires in California, House Speaker Nancy Pelosi's home state.
Mr Trump, however, acknowledged that such a move would likely trigger a legal battle ending in the Supreme Court.
Almost half of all Americans (47 per cent) say there is a serious problem at the border but decline to call it a crisis. The White House has not indicated if Trump would sign it.
Graham's comments are significant, given that he has been one of the president's biggest allies in Congress, steadfastly urging him not to back down on the wall or else risk an end to his presidency.
The concerns raised were those who have to continue working may not have time to find a temporary job for supplemental income and might not have much in savings to get through the shutdown.