Donald Trump's disapproval ratings have reached record highs as the president refuses to back down from his border wall funding demands, sparking the longest government shutdown in US history.

A new CBS News poll released on Wednesday shows the White House and GOP leadership are losing support for the president’s campaign promise of a wall sprawling the entirety of the US-Mexico border, with 71 per cent of voters saying they do not believe the issue is worth keeping the federal government closed.

Meanwhile, Mr Trump’s disapproval rating has reached an all-time high at 59 per cent — a figure that’s just one per cent higher than his previous record yet indicative of the president’s declining support amid the border wall battle.

The president offered a compromise over the weekend that was swiftly rejected by Democratic leadership in the US House of Representatives as it only provided temporary extensions to protections for certain undocumented immigrants, while handing him the $5.7bn he has demanded to begin building his wall along the southern border.

The same CBS News poll revealed Americans hold a far more favourable view of House Speaker Nancy Pelosi’s handling of the government shutdown, with 47 per cent of respondents saying the California Democrat has handled the negotiations better than the president, compared to 35 per cent favouring Mr Trump.

Ten per cent of those surveyed said neither politician was handling the shutdown negotiations well.

Meanwhile, just 28 per cent of respondents said Mr Trump’s border wall battle was worth keeping the government shutdown.

The poll was released on the 33rd day of the government shutdown — the 15th of its kind and the longest in American history.

Nearly 800,000 federal employees have remained without pay for four weeks, with many reporting difficulties keeping up with monthly bills, housing costs and other necessities. The FBI also released a 72-page report outlining the various issues agents are facing to keep up with investigations despite a lack of resources.

Six in 10 Americans said they felt the government shutdown was causing “serious problems” for the country, compared to 34 per cent who said the shutdown was causing “some problems” and just five per cent who said it was causing “no problems” at all.

It remains unclear what could spur the president to approve reopening the government. Mr Trump has walked back suggestions that he would invoke a national security crisis in order to effectively secure his funding for the border wall — a move that would face intense legal scrutiny and likely get blocked in the courts, but could allow lawmakers to separate the issue of immigration reform from ongoing negotiations to reopen the government.

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Lawmakers on both sides of the political aisle have suggested holding off on the border wall negotiations until once the government is reopened.