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 a meeting with Russell Vought, director of the US Office of Management and Budget (OMB), as they would be discussing which government activities should stop and which are essential.

The OMB director typically advises the president on furloughing employees and determining funding allocations during a shutdown.

Vought indicated that the White House had suspended billions meant for Democratic states, specifically targeting $18 billion in infrastructure projects in New York.

The divide deepened as Trump characterized the shutdown as a product of Democratic selfishness, while House Minority Leader Hakeem Jeffries accused Republicans of obstructing necessary healthcare provisions.

About 750,000 federal workers are projected to take unpaid leave, although essential personnel like law enforcement and air traffic controllers continue to work without pay. Tourist sites with federal funding face closures, impacting access to numerous historical attractions.