"They left town", he said of the Democrats during an appearance on "Fox & Friends".
Mulvaney also vouched for President Trump being hard at work, even as Congress essentially skipped town.
Asked about Trump's border-closing threat, Mexican President Andres Manuel Lopez Obrador told reporters it was an internal US government matter.
Revisiting footage of Trump's December 11 vow to take responsibility for a shutdown, Lemon reminded viewers that "the president owns" it "and the blame is all his", despite his current argument that Democrats are at fault.
Trump is also canceling plans to visit his Florida resort, Mar-a-Lago, and will remain in Washington over the New Year holiday, Office of Management and Budget Director Mick Mulvaney said.
Trump is now demanding $5 billion in funding for his proposed wall along the U.S. -Mexico border, but Democrats are only willing to give up to $1.6 billion for border security.
"And I think the reason they did is because Nancy Pelosi, in fairness, does not have the votes for the speakership yet".
The White House official said the president wants to close loopholes and expedite the asylum process by increasing the number of immigration judges. Hammill said Democrats are waiting for Trump to publicly endorse a proposal to end the shutdown because he "has changed his position so many times".
Democrats are considering several options once they take over the House next month: passing a short continuing resolution to fund the rest of the government, a long-term continuing resolution, or funding all of the government at current levels other than the Homeland Security Department, Politico reported earlier this week.
"We sat down with (Chuck) Schumer and gave him a number below five". Pat Roberts, R-Kan., who opened the Senate on Thursday for a session that only lasted minutes. "Do the Dems realize that most of the people not getting paid are Democrats?"
Trump asked for 500 to 550 miles of a wall or steel slats fence, saying other parts of the border already have natural barriers, such as mountains.
He has also repeatedly threatened to cut off USA aid to countries he deems insufficient partners in combating illegal immigration, but has thus far failed to follow through with those threats.
"Honduras, Guatemala and El Salvador are doing nothing for the United States but taking our money", Trump wrote in a tweet. It was unclear how Trump's threat to close the border would affect his efforts to ratify an amended North American free trade pact.
Taylor's inflatable rat, which sports a cellphone in one hand, a suit, red tie and Trump-like hair, is no stranger to the streets of D.C. The roughly 13-foot inflatable rat has been paraded around the nation's capital in the back of Taylor's specially altered 1970s Chevrolet pickup truck and has been seen near the White House, Trump's D.C. hotel, Capitol Hill and the courthouse.