Donald Trump was talking about concrete walls long before he became US President, but he's not always had the same stance.

On the same day, Trump travelled to the Mexican border to make his case for building a $US5.7 billion ($8.4 billion NZ) wall to keep illegal immigrants out of the US, a video resurfaced from 2004.

In it, Trump offers students at Wagner College on New York's Staten Island some advice.

"Don't give up," he told students at a commencement address. "Don't allow it to happen. If there's a concrete wall in front of you, go through it. Go over it. Go around it. But get to the other side of the wall."

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The video was shared by The Daily Show host Trevor Noah, who tweeted that Trump "better hope no one shows Mexico this old video we found".

Noah said Trump's video from 2004 has some relevance today.

"If there's one thing we know, it's that nothing will stop immigrants trying to come to America. This is a place that people dream of coming to … people trying to make a better, safer life for their families will do anything to achieve that dream."

The timing coincides with a big push by the President to secure support for the wall between the two countries.

A Republican politician in Montana is proposing to give more than $US8 million ($A11 million) to help build it, while South Dakota senators voted on Thursday to endorse the President's plans.

The resolution passed in the South Dakota Senate simply urges construction of a steel barrier. The separate $8 million proposal in Montana would have little chance of getting past a Democratic governor who is exploring a run for president.

Scott Sales, a fiscally conservative Republican who leads the Montana Senate, says his proposal is a "small token" to show border security "is of vital interest to all citizens regardless of what state they live in".

Mr Trump threatened on Thursday to declare a national emergency to circumvent Congress if he can't reach a deal with Democrats to fund the wall.

Speaking in Texas as the partial government shutdown dragged into a 20th day with hundreds of thousands of federal workers off the job or working without pay, Trump said he "will" declare a national emergency "if I have to", but is "not prepared to do that yet".

"So we're either going to have a win, make a compromise — because I think a compromise is a win for everybody — or I will declare a national emergency," he said.