By Donovan Slack
Copyright bbc
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.
It then gives directions to federal agencies about which employees to place on furlough, which means unpaid leave.
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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, including $18bn (£13.4bn) in infrastructure projects in New York – home of both Senator Chuck Schumer and the Democratic leader of the House of Representatives, Hakeem Jeffries.
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.
Lawmakers are expected to try again on Friday afternoon to resolve the impasse with a vote in the Senate.
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.