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.