"If we have to close down the country (over) border security, I actually like that in terms of an issue", he said.
Hours ahead of a White House summit with Democratic leaders, President Donald Trump on Tuesday demanded funding for his long-promised wall along the US southern border in a series of tweets filled with inaccuracies.
"I am pleased that we have reached an agreement which creates lasting institutional change for the Caucus", Sánchez said in a statement.
Trump's lawyer and former New York City mayor Rudy Guiliani told the Times that he would tell the president to fight any request for his tax returns. Just before the State of the Union in January, she cautioned Democrats to not get in the way of Trump being what she described as his "slobbering" self.
Government funding for some agencies is set to expire on December 21, threatening a partial shutdown. Mr Trump and Schumer jabbed at each other over the import of the midterm elections - and who will be blamed if a shutdown occurs.
House Democratic Leader Nancy Pelosi gave her weekly press conference Thursday. They are not willing to go above the current roughly $1.3 billion level of funding slated for border security.
Said Schumer outside the White House, "This Trump shutdown, this temper tantrum that he seems to throw, will not get him his wall and will hurt a lot of people". That is less than the $1.6 billion a bipartisan Senate committee has approved.
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After the meeting, Pelosi revealed to Democrats that Trump had claimed in their private session that Mexico would pay for the wall - his oft-stated campaign promise that he has abandoned since taking office.
"Today, Nancy Pelosi acquitted herself in a way that should put to rest any argument about whether she's up to that task", he said, alongside a chyron reading "Like a Boss" and a picture of Pelosi smiling in a pair of sunglasses.
The only Texas Democrat in the House to voice opposition to Rep. Nancy Pelosi's bid for speaker is standing down.
"I myself thought we would open the meeting with a prayer, which I did once we privately had the meeting outside the press - if you call that private because there were many people in the room", she said, according to the network.
"When the president brags he has won North Dakota and IN, he's IN real trouble", retorted Mr Schumer with a smile.
At another point in the talks, Mr. Trump got told off by Ms. Pelosi for suggesting that she was not free to speak her mind as she was yet to secure her place as Speaker of the House in the forthcoming Congress. White House spokeswoman Sarah Sanders said in a statement it was a "constructive dialogue" and said Trump was "grateful" the cameras captured him fighting to protect the border.