Meanwhile, a federal judge has laid out a path for the administration to fund SNAP benefits, which ran out on Saturday, saying the administration could tap more than $5 billion in emergency funds, as well as a much larger pot of tariff revenue collected by the Agriculture Department to fund the program.

As the government shutdown stretched into its second month, President Donald Trump claimed that a lapse in funding for the Supplemental Nutrition Assistance Program (SNAP) would mostly harm Democrats.

Christopher Bosso, a professor of food policy at Northeastern University and the author of a book about the history and politics of SNAP, said he was unaware of any studies that examined voting patte...