"This is a very important battle to win from the standpoint of safety, number one, [and] defining our country and who we are", Mr Trump told reporters at the White House before leaving for a short trip to the Camp David presidential retreat.
Vice President Mike Pence held a meeting with congressional leadership staff on Sunday afternoon, but after the meeting there was little indication they were getting close to a deal to reopen the government.
"I can relate", Mr Trump, a former NY businessman, said when asked if he could relate to the pain of federal workers struggling to pay their bills. "He'll face a challenge, I'm sure", Senator Dick Durbin, Democrat of IL, said Sunday on CBS's "Face the Nation". "Many of those people that won't be receiving a paycheck, many of those people agree 100% with what I'm doing".
The White House is demanding 5.7 billion dollars in border wall funding with Democratic lawmakers saying they will offer no more than 1.3 billion, and requiring a stipulation that no funds can go towards a wall.
Trump faces a messaging war with Democrats over the government shutdown fight, as Democrats began the new year sounding the alarm on how the partial shutdown is hurting Americans and government employees.
The White House said the letter, as well as details provided during the meeting, sought to answer Democrats' questions about the funding request.
Speaking with reporters outside of the White House, Trump said, "We'll obviously be discussing the wall, which is desperately needed". According to a Friday article by elections analyst Nathaniel Rakich from statistical website FiveThirtyEight, early poll numbers showed Americans overwhelmingly blaming Trump for the government shutdown.
President Trump has floated the possibility of declaring a national emergency to get a barrier built on the U.S. -Mexico border.
"There is a provision in law that says the president can declare an emergency".
The National Emergencies Act allows the president to declare a national emergency, providing a specific reason for it.
Mr Trump was "willing to take the concrete wall off the table", Mr Mulvaney told NBC. "I've never had this much support", said the president in a surprise briefing on Thursday. Asked about it on "Fox News Sunday", White House Press Secretary Sarah Huckabee Sanders said "whatever action he takes will certainly be lawful, and we're looking at every option". We are now planning a Steel Barrier rather than concrete.
House Armed Services Committee Chairman Adam Smith said the executive power has been used to build military facilities in Iraq and Afghanistan, but would likely be "wide open" to a court challenge for the wall along the U.S. -Mexico border. These workers typically receive back pay after a shutdown ends, but it is not guaranteed.
USA law allows him to direct military construction projects under those circumstances but the money would have to come from defence department funds and there would inevitably be legal challenges by the Democrats that would drag out the matter. And hundreds of government scientists say they will miss crucial opportunities to exchange research and ideas because the shutdown is stopping them from attending major scientific conferences about technology, space exploration and climate change.