President Donald Trump has stated 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 are working without pay. Some federal attractions have closed to visitors while others, including the Statue of Liberty, remain open.

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

Trump's meeting with Russell Vought, director of the US Office of Management and Budget (OMB), left many uncertain about what decisions might be made regarding halting government activities.

In dueling press conferences on Capitol Hill, neither party appeared willing to give ground. House Speaker Mike Johnson accused Democrats of selfishness, while Minority Leader Hakeem Jeffries called out the Republicans for their reluctance to support working-class Americans with healthcare provisions.

As the political standoff continues, over 750,000 federal employees are expected to take unpaid leave, and essential services are being disrupted, leading many to anticipate visible impacts on their lives and potentially more pressure on Congress to reach an agreement.