Callers to the White House have been greeted with an answering machine message saying the phone line is closed because opposition Democrats are "holding Government funding hostage".

The message follows an unsuccessful vote to extend Government funding for a month while a long-term budget bill can be worked out between Republicans and Democrats, who say any bill must include protections for "Dreamers".

The resulting shutdown means non-essential services including major landmarks, many civilian military personnel and White House phone lines are unmanned because wages can not be paid.

The White House has blamed the shutdown on Democrats, calling them "obstructionist losers" and accusing them of being more interested in illegal immigrants than in national security.

"They could easily have made a deal but decided to play shutdown politics instead," President Donald Trump said.

Over the weekend, Americans calling the White House comments line discovered it was repeating this message:

"Thank you for calling the White House. Unfortunately, we cannot answer your call today because congressional Democrats are holding government funding — including funding for our troops and other national security priorities — hostage to an unrelated immigration debate. Due to this obstruction, the Government is shut down. In the meantime, you can leave a comment for the president at www.whitehouse.gov/contact. We look forward to taking your calls as soon as the Government re-opens."

Recordings of the message were shared on social media along with commentary on what it says about the Trump administration.

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Some went beyond disbelief to anger, calling the message not childish but un-American:

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And, predictably, calling on Mr Trump to resign:

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Some questioned the ethics or even the legality of the message:

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For others, it was a call to arms:

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But the Government also had its supporters, who applauded the message and defended its accuracy:

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An emerging deal, kick-started by a meeting of about two dozen Republican and Democratic centrists, appeared to involve reopening the Government by Monday morning in return for a promise by majority Republicans to deal with Democrats' immigration concerns in coming weeks.

Democrats say short-term spending legislation must include protections for illegal immigrants brought to the United States as children, known as "Dreamers".

But Senate negotiators failed to reach an agreement late on Sunday to restore federal spending authority, meaning the US government shutdown will enter its third day.

Senate Majority Leader Mitch McConnell has offered an olive branch to Democrats, pledging on the Senate floor to bring immigration legislation up for debate in February if the issue is still unresolved by then.

The Senate has set a vote for 12:00pm on Monday (4:00am on Tuesday AEDT) on advancing a measure to provide temporary government funding through to February 8.