He added the president has to keep his campaign promise he would build a wall along the nation's southern border, but declaring the situation a national emergency would set up a risky precedent.
The president said his lawyers have advised him "100 percent" that he can fund his border wall via a national emergency declaration.
Mr. Trump's insistence on billions of dollars in funding to keep a signature campaign promise - and Democrats' insistence to fund the government without wall funding - mean the partial government shutdown is poised to be the longest government shutdown in usa history. "If you look, Democrats, in Congress, especially the new ones coming in, are starting to say, 'Wait a minute, we can't win this battle with Trump, because of the fact that it's just common sense".
Donald Trump Jr., the president's son, said Acosta's video was one of the "best self-own videos", showing that "walls work".
The Republican president is adamant that a government funding bill to end the shutdown include $5.7 billion for a border barrier - his signature campaign promise.
That has resulted in a partial government shutdown now in its 20th day, with hundreds of thousands of federal employees - including air traffic controllers, the FBI and Coast Guard - going without pay.
Senate Minority Leader Charles E. Schumer, D-N.Y., emerged from the West Wing and accused Trump of slamming the table around which he and leaders were sitting before, as Speaker Nancy Pelosi, D-Calif., put it, "stomping out".
"I would like to do a much broader form of immigration", he said in Texas. Using the Internet archiving tool Wayback Machine, CBS News obtained the now-deleted memo the Trump campaign posted in April 2015 describing how the US would compel Mexico to make a "one-time payment" of $5 or $10 billion for the wall. President Trump insisted on Twitter.
Three weeks into the crisis, Most Americans appear to be blaming Trump for the shutdown - further isolating the president with only his ardent supporters in favor of the White House strategy.
Trump tweeted that he will not attend the World Economic Forum in Davos, Switzerland, later this month "because of the Democrats' intransigence on border security".
In Washington, federal workers denounced Trump at a rally with congressional Democrats, demanding he reopen the government so they can get back to work.
"We should be able to make a deal with Congress", the president said. The President hasn't been blamed in any of the previous shutdowns.
Trump has started to claim that he never said during his election campaign that Mexico would directly pay for the wall: "Obviously, I never said this, and I never meant they're going to write out a check", the president told reporters at the White House on Thursday.