Outgoing White House Chief of Staff John Kelly contradicted the president, telling the Los Angeles Times, "to be honest, it's not a wall". Recently, Trump has taken to describing a wall made of "steel slats".
Trump said in a Twitter post that border security can not exist "without a strong and powerful Wall".
"I am in the White House waiting for the Democrats to come on over and make a deal on Border Security", he posted to social media early Monday morning.
So did President Trump make the right call to shut down the government during the remaining days of a Republican-controlled Congress?
The president continued to insist he wants to build a wall along the US-Mexico border, despite the assertions of three confidants.
A former Homeland Security secretary, Mr Kelly is well versed in the complexities of immigration and border security and his views seemingly contrast with Mr Trump's harsh rhetoric on migration. There may be steel slats.
Costello, indeed, believes Democrats are dug in on the border wall - and unlikely to cave.
The first bill, sources say, will include year-long funding plans for every government agency now closed, with the exception of the Department of Homeland Security.
As the partial shutdown drags on and federal workers feel the pinch, some lawmakers have suggested that funds for a physical barrier on the border could be coupled with other immigration measures favored by Democrats, such as legal status for so-called Dreamers, young immigrants brought to the USA illegally as children.
"For those that naively ask why didn't the Republicans get approval to build the Wall over the a year ago, it is because IN THE SENATE WE NEED 10 DEMOCRAT VOTES, and they will gives us "NONE" for Border Security!", he tweeted.
In one of his many tweets since the shutdown started, Trump wrote: "We will be forced to close the Southern Border entirely if the Obstructionist Democrats do not give us the money to finish the Wall & also change the ridiculous immigration laws that our Country is saddled with".
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- Senate compromise revived: Lawmakers could revive a deal reached in August by Shelby and top Appropriations Committee Democrat Patrick Leahy to provide $1.6 billion for border barriers, including about 65 miles (105 km) of pedestrian fencing near the Rio Grande River.
Outgoing White House chief John Kelly said he had "nothing but compassion" for undocumented migrants crossing into the United States and undercut the idea of a border wall in an interview Sunday that jarred with President Donald Trump's tough rhetoric on immigration.
"This is the same president who repeatedly promised the American people that Mexico would pay for the wall that he plans to build", New York Rep. Hakeem Jeffries said on ABC's This Week program. Richard Shelby (R-AL). "I wish it were not so", Alabama Sen. Central Americans are also deeply integrated into the USA economy, often performing physically demanding, low-pay jobs in construction, agriculture and other vital sectors.
Trump has ordered an end to existing protection for the young immigrants, known as "Dreamers", and those seeking temporary refuge from Sudan, Nicaragua, Haiti and El Salvador, but federal courts have stopped those moves pending further appeals. "It's morally irresponsible and it's got to stop", he said.
Democrats have resisted giving him anything - which eventually caused a partial government shutdown starting on December 22. "He's in the - he's in the White House".
Currently, an estimated 54,000 Customs and Border Protection agents and customs officers with DHS are working without pay as the shutdown continues into the New Year.
"The first bill would reopen all government agencies except for the Department of Homeland Security".
"While President Trump drags the nation into Week Two of the Trump Shutdown and sits in the White House and tweets, without offering any plan that can pass both chambers of Congress, Democrats are taking action to lead our country out of this mess", Schumer and Pelosi said in a joint statement.
Congress is in recess for the New Year's holiday but will reopen on Thursday, while Trump has stayed in the White House through the year-end festivities, shelving his annual vacation to his private Florida golf resort amid the impasse.
But even that may be hard without a compromise because the Senate will remain in Republican hands and Trump's signature will be needed to turn any bill into law. But at least one Senate Republican says it's time to move past the blame game. Shelby said. "It's not a question of who wins or loses".