WASHINGTON — If the government shutdown continues into November, about 42 million low-income people could face severe disruptions to their food stamp benefits, the Agriculture Department warned in a letter to state agencies last week, saying that the federal government would have “insufficient funds.”

More than a dozen states have since warned that food stamp recipients may experience significant delays in obtaining benefits next month, see their aid reduced or not receive assistance at all.

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The letter, a copy of which was obtained by The New York Times, said that the Agriculture Department’s Food and Nutrition Service, which operates the food stamp program, known as the Supplemental Nutrition Assistance Program, or SNAP, was exploring contingency plans. But it di

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