No one budged at US President Donald Trump's White House meeting with congressional leaders today, so the partial government shutdown persisted through a 12th day over his demand for billions of dollars to build a wall along the US border with Mexico.

They'll try again on Saturday.

In one big change, the new Congress convenes tomorrow with Democrats taking majority control of the House, and Democratic leader Nancy Pelosi said outside the White House that there would be rapid passage of legislation to re-open the government — without funds for the border wall.

But the White House has rejected that package, and Trump said ahead of the session with the congressional leaders that the partial shutdown will last "as long as it takes" to get the funding he wants.

"Could be a long time or could be quickly," Trump said during lengthy comments at a Cabinet meeting at the White House, his first public appearance of the New Year.

Democrats said they asked Trump directly during the private meeting held in the Situation Room why he wouldn't consider their package of bills.

One measure would open most of the closed government departments at funding levels already agreed to by all sides. The other would provide temporary funding for Homeland Security, until February 8, allowing talks to continue over border security.

"I said, Mr President, Give me one good reason why you should continue your shutdown," Senate Minority Leader Chuck Schumer said afterward. "He could not give a good answer."

Added Schumer, "We would hope they would reconsider."

House Republican leader Kevin McCarthy said there's no need to prolong the shutdown and he was disappointed the talks did not produce a resolution.

He complained that Democrats interrupted Homeland Security officials who were trying to describe a dire situation at the border.

"We were hopeful that we could get more of a negotiation," said McCarthy.

He said the leaders plan to return to the White House to continue negotiations.

The two sides have traded offers, but their talks broke down ahead of the holidays. Today, Trump also rejected his own Administration's offer to accept US$2.5 billion for the wall. That offer was made when Vice-President Mike Pence and other top officials met Schumer at the start of the shutdown.

Instead, Trump repeatedly pushed today for the US$5.6 billion he has demanded.