Trump has demanded $US5 billion ($A7 billion) as a down payment on construction of a huge wall he argues is the only way to keep illegal immigrants and drugs from entering the United States.

"Anytime you hear a Democrat saying that you can have good Border Security without a Wall, write them off as just another politician following the party line!" Trump wrote in a Twitter posting on Monday.

"Time for us to save billions of dollars a year and have, at the same time, far greater safety and control."

Democrats and some Republicans argue there are less costly, more effective border controls.

The money Trump wants is a fraction of the roughly $US450 billion Congress was poised to approve - before the latest battle over the proposed wall - to fund several agencies that will otherwise run out of money on Friday.

Large swaths of the government already are funded through next September, including the US military and agencies that operate public healthcare, education and veterans' programs.

Last Tuesday, Trump and leading congressional Democrats battled each other in front of television cameras in the White House Oval Office.

"I am proud to shut down the government for border security," Trump told House of Representatives Democratic leader Nancy Pelosi and Senate Democratic leader Chuck Schumer.

Since then, a senior House Republican aide said his party was "in a pickle" over how to keep the government open.

The aide noted that Republicans, who will control both houses of Congress until January 3, will not be able to muster the minimum 218 votes needed in the House to pass a funding bill if it contains Trump's demand for border wall money.

If funds run out, the NASA space program would potentially be unfunded, along with national parks, the US diplomatic corps and agriculture programs.

Australian Associated Press