Rusty Long is debating which bills to pay and which to hold off on, as he plans to miss his first paycheck on Friday, along with hundreds of thousands of other federal employees.

An architect for the Agriculture Department, the 36-year-old recently moved to Cary, N.C., from Portsmouth, Va., for better schools for his son, who has cerebral palsy. His wife stays at home with their four children, including a 4-month-old baby, meaning Mr. Long’s paycheck is their only income.

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