The moves indicate the Republican president has no intention of backing off his pledge to build a wall that he believes will stem illegal immigration and drug trafficking.
A source in the meeting said the weekend talks were good only in the sense that they got a more precise sense of what the administration wanted. Rep. Adam Smith (D-Wash.), chairman of the House Armed Services Committee, told CNN on Monday that while Trump could declare such an emergency, it would nearly certainly be challenged in court.
The shutdown has left some 800,000 federal workers sent home or working without pay.
Trump has said in recent days that he might seek to unilaterally secure border wall funding by declaring a national emergency, a move that experts say would be of questionable legality.
A first round of talks between White House officials and congressional aides has made little progress toward ending the government shutdown, with each side accusing the other of giving no ground.
It was not immediately clear whether all the major TV networks had agreed to the White House's request to hand over a section of their prime-time schedule.
Trump also asserted that he could relate to the plight of the hundreds of thousands of federal workers who aren't receiving paycheques, though he acknowledged they will have to "make adjustments" to deal with the shutdown shortfall.
"What I'm aware of is they're looking at it and the president is considering it", Pence said.
Trump skipped a planned trip to Florida to stay in the USA capital during the Christmas and New Year's holiday after large chunks of the federal government were shuttered on December 22. And it repeats some existing funding requests for detention beds and security officers, which have already been panned by Congress and would likely find resistance among House Democrats.
Trump's announcement follows news from White House press secretary Sarah Sanders that the president will travel to the border on Thursday.
With the talks stalled, Pelosi, a California Democrat, said House Democrats meant to start passing individual bills to reopen agencies.
The presidential comment came soon after US Vice President Mike Pence held a meeting with representatives of the top Democratic Congressional leaders - House Speaker Nancy Pelosi and Senate Minority Leader Chuck Schumer.
Trump contends the wall is needed to stop migrants from illegally crossing into the US from Mexico, as well as preventing drug trafficking and terrorism.
"We can call a national emergency because of the security of our country" to guard against the threat that border officials say is posed by illegal crossings, Trump said.
Democrats say other border security measures are more efficient and cost-effective than a wall, which they say is contrary to American values.
Mr Trump tweeted there was "not much headway made" in talks with Democratic Party representatives on Saturday.
And according to a new report, Trump is continuing in this destructive and counterproductive tactic for one main reason: He doesn't want to look like a loser.
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