Its total estimated cost is US$23 billion ($32 billion).
Trump also promised his wall would be so strongly built only an Olympic champion could get over it.
Trump's 39 percent approval rating matches the lowest point of his popularity, in August 2017, when he condemned "many sides" for the Unite the Right rally in Charlottesville, Virginia, where a white nationalist drove a auto into a group of protesters, resulting in the death of Heather Heyer, 32, and causing injuries to 19 others.
White House spokeswoman Sarah Sanders accused Democrats of "openly choosing to keep our government closed to protect illegal immigrants rather than the American people". But he was ignored and his microphone was soon cut off.
Next up will be a Senate pro forma session on Monday, the last legislative and calendar day of the year.
"I can't tell you when the government is going to be open", he said. I'll call it whatever they want ... "This is the way they've been running this place".
During the shutdown, the Washington Post estimated that about $200 million in economic activity would be lost each day the shutdown continued.
While its impact has been limited so far, partly due to numerous 800,000 or so federal workers affected being on holidays, that could change soon.
Trump vows no end to shutdown until wall funded
He adds that the shutdown has a dire impact on many NFFE employees living paycheck-to-paycheck. Trump told reporters after meeting with USA service members in Iraq on Wednesday.
China says detention of Canadian involves employment issue
A Canadian lawmaker said Wednesday that the case involved visa irregularities for an Alberta woman who had been teaching in China. Canadians who study or do business in China may want to lie low and keep a low profile, she said. "One detention is bad enough".
Gianfranco Zola opens up about Eden Hazard’s future at Chelsea FC
"That is the target, and we are going to approach that game by training very hard and we look forward to that game. Eden Hazard has the potential to become Chelsea's greatest player ever according to Gianfranco Zola .
With no end to the shutdown in sight, the Office of Personnel Management sent out a Twitter posting Thursday morning in which it shared advice and letter templates for federal workers to use in negotiating for deferred rent and payments to other creditors.
So far, neither side has been willing to negotiate, leaving roughly 25 percent of the government without funding.
Candice Nesbitt, 51, has worked for 1 ½ years for the U.S. Coast Guard, the only branch of the military affected by the shutdown.
Having failed to procure wall funding when his party controlled both houses of Congress, it was unclear how Trump meant to carry the day with Democrats partially in charge.
Rep. Mark Meadows, a North Carolina Republican who's a close ally of the President's and chairman of the conservative House Freedom Caucus, said Wednesday that Trump's resolve to get $5 billion for border security is "very firm". New members will join from January 3 making Democrats the majority in House of Representatives.
At that time, Mr McGovern said, Democrats expect to offer a spending measure "plus probably disaster relief funding".
The House and Senate were expected to convene Thursday for the first time since leaving Washington, D.C., for the holiday break. "But at the 11th hour, Trump scuttled the agreement because it did not provide additional funding for a border wall".
The Democrats mistakenly assume that the public overwhelmingly views the partial shutdown as a crisis even though it doesn't affect that many Americans in relative terms, he said.
The Reuters/Ipsos poll was conducted online in English across the United States.
The online poll was conducted December 21-25 by Reuters/Ipsos among 2,440 adults, including 946 Democrats and 846 Republicans, with a margin of error of plus or minus 2 percentage points.