Senate majority leader Mitch McConnell, speaking on the Senate floor, said no votes would be held until a deal is struck by Democrats and the White House. That meeting ended after 30 minutes with no resolution.
President Donald Trump praises himself as "doing great" but also complains that "it's war every day" in the White House.
The White House did not immediately respond to a request for comment from Newsweek on Monday.
But what appeared to spook Wall Street most was Trump's continuing tirade against Federal Reserve Chairman Jerome Powell, whom the president reportedly considered ousting over fed policy raising interest rates.
Governor Ralph Northam of Virginia - a state bordering the U.S. capital that is home to many federal employees - urged Mr Trump in a letter yesterday to push immediate action to end the shutdown, saying it "inflicts real harm" on workers.
Nancy Pelosi, the top Democrat in the House, also warned on Saturday that the shutdown may not be resolved until early January, when her party takes control of the chamber.
Jeff Merkley says Democrats are "absolutely willing" to commit taxpayer dollars for border security.
Now, that gridlock is affecting large parts of the federal government.
ASSOCIATED PRESS Border wall prototypes stand in San Diego near the Mexico US border seen from Tijuana Mexico
Nine of 15 federal departments, including State, Homeland Security, Transportation, Agriculture and Justice began partially shutting down after funding for them lapsed at midnight (05:00 GMT Saturday). The Securities and Exchange Commission has posted a list of the services it will soon suspend, including the processing of certain business records.
Customs and border staff will keep working, although their pay will be delayed. More than 400,000 "essential" employees in those agencies will work without pay until the dispute is resolved. After every previous shutdown, Congress has passed legislation to retroactively pay employees.
Trump made a Mexico border wall one of his main campaign promises and the idea is popular with many Republicans backing the president's message that illegal immigration is out of control. Like Mattis, the special presidential envoy for the Global Coalition to Counter ISIS resigned in protest of Trump's decision to pull USA troops from Syria.
"We're on duty 24-7, 365 days a year", said Capt. Cameron Hillier, spokesman for NORAD and U.S. North Command. Trump seemed set to approve but then backtracked, apparently under the influence of rightwing media furious at his abandonment of a key campaign pledge, if disregarding his repeated vows that Mexico, not the United States taxpayer, would pay for his promised wall. This past week he said he would be "proud" to close down the government.
Mr Trump had said any impending shutdown could last "a very long time" as he blamed Democrats over the failure to agree a deal on spending.
An angry US President Donald Trump complained on Monday that he was "all alone" in the White House as the US government shutdown hit a third day, even plunging the nation's main Christmas tree into darkness.
"In the Democrats' mind, that is not a wall". Conversations last night did occur.