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.

On the first day of the shutdown, Vought said the White House had moved to pause or cancel billions of dollars in funding meant for Democratic states.

Republicans want to pass a funding measure without anything else attached, but Democrats want to include a renewal of health insurance subsidies for low-income individuals set to expire at the end of the year.

As politicians traded barbs, US government services started to grind to a halt with about 750,000 federal workers expected to take unpaid leave according to the Congressional Budget Office (CBO).

Federal employees deemed essential continued to work, though without pay, and air travel was not immediately affected. Meanwhile, museums and attractions were turned away visitors, impacting tourism significantly.

Both parties will need cooperation to pass funding measures and reopen the government, with discussions expected to continue regarding the ongoing stalemate.