More than 40 million Americans use the Supplemental Nutrition Assistance Program (Snap) to feed themselves and their families.
While that programme had enough funding to survive the first four weeks of the shutdown, the Trump administration has said the money will run out on 1 November.
By Saturday, Snap benefits, also called food stamps, could lapse for the first time in the programme’s history.
Snap is a critical lifeline that keeps families out of poverty, Hannah Garth, a Princeton University professor who studies food insecurity, told the BBC.
Groups that provide food for people in need are already under strain and the loss of Snap will make the situation worse, she added.
On Thursday, New York Governor Kathy Hochul declared a state of emergency so the state could “help the three million New Yorkers losing food assistance” because of the shutdown.
People enrolled in Snap have been stockpiling food and visiting aid organisations, as they wait for the impasse to lift on Capitol Hill.
Half the states and the District of Columbia have sued President Donald Trump’s administration over the food aid freeze.
The administration, in turn, has blamed Democrats for the funding running dry and said it will only draw from a Snap contingency fund in an emergency such as a natural disaster.
The federal government distributes Snap benefits through programmes run by the states.
Some states, such as Virginia, have said they will be able to make up for any lack of funds in November, but others like Massachusetts have said they can’t cover the shortfall.
