President Donald Trump has said he and his budget director will work out which Democrat Agencies to cut as the US government shutdown approached its third day.

He suggested Republicans should seize the opportunity to clear out dead wood and gave no hint of concessions to Democratic demands that legislation funding the government should include healthcare insurance subsidies.

Republicans and Democrats on Capitol Hill, meanwhile, continued to blame each other for failing to keep federal agencies open.

Hundreds of thousands of federal workers are staying home, while others worked without pay. Some federal attractions closed to visitors while others, including the Statue of Liberty, stayed open.

Analysts don't expect either side to budge without pressure from everyday Americans, most of whom have yet to feel direct impacts on their lives.

It was unclear exactly what Trump could decide in Thursday's meeting with Russell Vought, director of the US Office of Management and Budget (OMB).

When Congress fails to keep the US government open, the OMB director works with the president to pick which government activities should stop and which are essential.

Both sides must come together to pass legislation if the government is to reopen. Republicans need eight Democratic senators to vote with them, while Democrats need 13 Republicans to side with them. Only three Democrats joined with Republicans on the last failed vote in the Senate on Wednesday.

As the political blame game escalates, the shutdown's impacts on federal services and the workers tasked with maintaining them increasingly come into focus.