US President Donald Trump says if the government shutdown stalemate continues, Republicans should fund the government by changing Senate rules, which currently require a super-majority for appropriations bills to pass.

"The Dems (Democrats) just want illegal immigrants to pour into our nation unchecked. If stalemate continues, Republicans should go to 51 per cent (Nuclear Option) and vote on real, long term budget," Trump said on Twitter on Sunday.

Trump's proposal was almost immediately rejected by Senate Republican Leader Mitch McConnell.

Senate Republicans oppose changing the chamber's rules so that legislation to fund the government and end the current shutdown could pass with a simple majority, the spokesman said.

"The Republican Conference opposes changing the rules on legislation," the spokesman said in an email.

Current Senate rules require a super-majority of three-fifths of the chamber, usually 60 out of 100, for legislation to clear procedural hurdles and pass.

Funding for federal agencies ran out on Saturday with Trump and Republican lawmakers locked in a stand-off with Democrats. There appeared to be no clear path for a quick end to the crisis.

Democrats say short-term spending legislation must include protections for illegal immigrants brought to the US as children, known as "Dreamers". Republicans, who have a slim 51-49 Senate majority, said they would not negotiate on immigration until the government was reopened.

Meanwhile Vice President Mike Pence said on Sunday the Trump administration would not reopen talks with Democratic lawmakers on "illegal immigration" until the US government shutdown had concluded.

During remarks to troops at a military facility in the Middle East, Pence said Democrats were playing politics with military personnel pay.

"We're going to demand that they reopen the government," Pence said. "In fact, we're not going to reopen negotiations on illegal immigration until they reopen the government and give you, our soldiers and your families, the benefits and wages you've earned."