"Look, if Harry Truman couldn't nationalize the steel industry during wartime, this president doesn't have the power to declare an emergency and build a multibillion-dollar wall on the border", the California Democrat said on CNN's "State of the Union".
"Democrats and now a growing number of Republicans are coming together and saying let's open up the government and debate border security separately", Schumer told reporters in NY.
With the partial shutdown in its third week, House Speaker Nancy Pelosi said she intends to begin passing individual bills to reopen agencies in the coming days, starting with the Treasury Department to ensure people receive their tax refunds.
The debate was 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. Trump wants to erect steel and/or concrete walls over 30 feet tall on more than 200 miles of the border that would include new and replacement barriers. The Democrats said the new bill will exclude Trump's request for $5 billion for funding US-Mexico border wall. Trump suggested Sunday that he, Pelosi and Senate Minority Leader Chuck Schumer could find compromise "in 20 minutes, if they want to".
"This shutdown could end tomorrow or it also could go on for a long time", Trump said Sunday. He said Trump had painted himself into a corner and needs to "figure out how he unpaints himself from that corner".
He later tweeted that the Pence talks were productive. Trump had previously promised a concrete wall, but now says it could be made of steel slats.
One of the officials says no new meetings have been scheduled. Trump said he wanted to help on the Dreamer issue but preferred to wait for a Supreme Court ruling on it first.
Congressional Democrats have vowed not to give the USA leader any money for the wall.
"The president is interested in resolving this issue", Mulvaney said.
Large chunks of the federal government were shut down on December 22 after lawmakers and the president hit an impasse over Trump's demand that a bill to keep the federal government operational include money to help build a $23 billion wall along the USA border with Mexico.
The shutdown has left transportation security agents and Federal Bureau of Investigation employees, among many others, working without pay.
"Mr. President, can you relate to the pain of federal workers who can't pay their bills?" the journalist asked Trump as he stood outside the White House. "And I'm sure that the people that are toward the receiving end will make adjustments, they always do. I thought it was highly disrespectful to the United States of America", Trump said.
In an interview with NBC's "Meet the Press", set to air Sunday, Mulvaney argued that the administration was willing to deal. Thom Tillis, R-North Carolina, in an opinion piece in The Hill on Friday called for a compromise on border wall funding that gives a pathway to citizenship for young adults brought to the USA illegally as children, also known as "Dreamers". This shutdown comes just as the Democrats are assuming control of the House after eight years of GOP rule, adding poison to a relationship with the White House that was fated to be sulfurous under the best of circumstances.
"We need to open up government and then negotiate. Not the other way around", Hoyer said.