Donald Trump's former lawyer Michael Cohen says he is postponing his testimony because of "ongoing threats" by the President.

Cohen was due to testify before Congress in February but said he would put it on hold because of concerns about his family's safety, according to his adviser Lanny Davis.

Davis cited "ongoing threats" against Cohen's family from Trump and the President's lawyer Rudy Giuliani as recently as this weekend, in the decision to postpone his February 7 appearance before the House Oversight Committee.

The White House, Giuliani and the committee have not yet commented.

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"Mr Cohen volunteered to testify before the House Oversight Committee ‪on February 7th," Davis said. "Due to ongoing threats against his family from President Trump and Mr. Giuliani, as recently as this weekend, as well as Mr Cohen's continued co-operation with ongoing investigations, by advice of counsel, Mr Cohen's appearance will be postponed to a later date."

"Mr Cohen wishes to thank Chairman Cummings for allowing him to appear before the House Oversight Committee and looks forward to testifying at the appropriate time. This is a time where Mr Cohen had to put his family and their safety first."

It comes the week after BuzzFeed claimed Trump told Cohen to lie to Congress over talks regarding a possible Trump Tower Moscow. The President has repeatedly denied having any business dealings with the Russians.

Special Counsel Robert Mueller released a rare statement following the article's release, disputing what was reported. "BuzzFeed's description of specific statements to the Special Counsel's Office, and characterisation of documents and testimony obtained by this office, regarding Michael Cohen's Congressional testimony are not accurate," wrote spokesman Peter Carr.

BuzzFeed says it stands by the story.

Meanwhile, Trump insisted he will push ahead with his State of Union address despite Nancy Pelosi asking him to wait until the US government reopens.

The US President said it would be "so very sad" not to deliver the speech in the House of Representatives — which sets the agenda for the year — as the record government shutdown entered day 33.

Cohen cancelled his testimony to Congress, citing 'ongoing threats' from Mr Trump and lawyer Rudy Giuliani. Photo / AP
Cohen cancelled his testimony to Congress, citing 'ongoing threats' from Mr Trump and lawyer Rudy Giuliani. Photo / AP

The Democratic speaker of the House of Representatives had suggested he should either delay the address or give it in writing, citing security concerns with the partial shutdown in its second month.

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Trump said in a letter to Pelosi on Wednesday local time that he would "be honouring" her original invitation to give the speech on January 29, "to deliver important information to the people and Congress of the United States of America regarding the State of our Union."

It puts Pelosi in a tricky position. She could now uninvite him from giving the speech, forcing him to give his address in another setting, such as at a campaign-style rally.

The pair have reportedly not spoken directly in two weeks, with Trump cancelling Pelosi's trip to see troops in Afghanistan after her suggestion he delayed his State of the Union address.

Meanwhile, Senate majority leader Mitch McConnell scheduled two votes on proposals to reopen the government for Thursday local time. Both funding proposals are doomed to fail, since they do not have bipartisan support — with CNN calling the "show votes" a "theatrical effort to make it look like they are doing everything possible" to end the impasse.

However, many believe the apparent "farce" could be the first step towards a solution, triggering negotiations to find a middle ground.

Trump had offered a three-year extension on protections for 700,000 undocumented young migrants in return for a $US5.7 billion ($A8 billion) wall funding.

Democrat James Clyburn yesterday suggested it might be "doable" to give the President money for a "humane wall" in return for permanent protections for Deferred Action Childhood Arrivals and immigrants with temporary protective status.

Democratic Speaker of the House of Representatives Nancy Pelosi had asked the US President to delay his speech as the record-breaking shutdown continues. Photo / AP
Democratic Speaker of the House of Representatives Nancy Pelosi had asked the US President to delay his speech as the record-breaking shutdown continues. Photo / AP

Senior officials in the White House have been discussing a proposal to give a path to green cards to the 700,000 DACA recipients over the past 24 hours, Axios reported.

Republican senators, including James Lankford, support the idea, while Jared Kushner told White House staff it could be a way to end the stand-off.

Kushner has been leading congressional negotiations with Vice President Mike Pence.

Democratic Senator Sherrod Brown told MSNBC's Morning Joe on Wednesday that no matter what his party offered, the President was "not going to end this".

He warned Trump could shut the government down again to fund the wall, which he forecast would cost $US30 billion — far more than the $US5.7 billion the President has requested so far.

"I think it's a question of the pressure builds and there's a tipping point where Republicans think, 'My gosh we can't keep doing this, because the public blames them. The public blames all of us, I get that."

"He's dug in on a proposal the country doesn't support. We know the President is always about dividing people an upending things and preaching his phony populism.

"People are beginning, even people who voted him, to see he has betrayed workers."

Republicans hold a 53-47 majority in the Senate but would need seven Democrats to reach the 60-vote threshold for Trump's bill to be passed — and are unlikely to get more than three or four.