US President Donald Trump met top Democratic lawmakers on Wednesday, but they failed to hammer out an agreement that would end a partial government shutdown over his demand for billions of dollars to build a border wall with Mexico.

One day before Democrats take over the House of Representatives, Trump showed no signs of backing away from his insistence that Congress cough up $5.6 billion for his "beautiful" southern wall.

Trump met behind closed doors at the White House with Nancy Pelosi, the Democrat who will take over as speaker of the House on Thursday, and Chuck Schumer, the Senate minority leader, but there were no indications any progress had been made in resolving the impasse.

"We asked the president to support the bills that we support that will open up government," Schumer said. "I asked him directly, I said 'Mr. President give me one good reason why you should continue your shutdown.'

"He could not give a good answer," Schumer said.

Republican Kevin McCarthy, who will be minority leader in the next House, said Democratic and Republican leaders of Congress would return to the White House on Friday for more talks.

"This doesn't need to go on very much longer," McCarthy said.

But Trump said he was prepared to hold out "as long as it takes" to secure the money he is seeking for the border wall.

"This is national security we're talking about," he said at a cabinet meeting ahead of the meeting with Pelosi, Schumer and top Republicans. "It's too important a subject to walk away from.

"I think the people of this country think I am right," Trump said, adding that it "could be a long time" before the government reopens.

Trump's meeting with Pelosi and Schumer was his first since an acrimonious Oval Office meeting with the pair on December 11.

Democrats say the border wall, one of Trump's key campaign promises, is a distraction from more complicated immigration problems and a tool for Trump to whip up support among his conservative base.

The standoff resulted in hundreds of thousands of federal employees being furloughed over the Christmas and New Year holidays -- and for the foreseeable future until a deal is reached.

- Romney hits out at Trump -

Amid the stalemate over the wall, Trump shelved his annual Christmas vacation in Florida, choosing to remain in Washington and fire off a stream of angry -- and often misleading -- tweets.

"Much of the Wall has already been renovated or built," he asserted, along with the dubious claim that Mexico would pay for the wall through the new trade deal between the two countries.

White House spokeswoman Sarah Sanders accused Democrats of refusing to compromise.

"President Trump made a serious, good faith offer to Democrats to open the government, address the crisis at our border and protect all Americans," Sanders said.

Pelosi is proposing a plan that would fund most government agencies through September 30 with the exception of the Department of Homeland Security, which oversees border security and would only receive funding through February 8.

Sanders described that approach as a "non-starter because it does not fund our homeland security or keep American families safe from human trafficking, drugs and crime."

Republicans lost 40 seats and their majority in the House in the November midterm elections but they retained control of the Senate by a slim margin.

Sixty votes, however, are needed to advance legislation in the Senate, requiring Democratic support.

Democratic Senator Chris Coons of Delaware welcomed the face-to-face meeting between Trump and Democratic leaders and told CNN he hoped it would lead to a end to what he called a "senseless" shutdown.

Republican Mitch McConnell, the Senate majority leader, has said he will only schedule a vote on a deal that has the support of both the House and Trump.

Adding to the uncertainty in Washington, an incoming senator, former Republican presidential candidate Mitt Romney, lashed out at Trump on Tuesday in an opinion piece in The Washington Post.

"Trump's words and actions have caused dismay around the world," wrote Romney, who was elected to the Senate in November from his home state of Utah.

"I do not intend to comment on every tweet or fault," Romney said. "But I will speak out against significant statements or actions that are divisive, racist, sexist, anti-immigrant, dishonest or destructive to democratic institutions."

Trump expressed surprise over the comments said he hoped the Republican senator would prove to be a "team player."

In an interview with CNN, Romney said he would vote to provide funding for a border wall. (AFP)