KEENE, N.H. — One day last month, in the middle of a furniture factory here, Hillary Rodham Clinton finished prepared remarks about her presidential candidacy and opened the floor for discussion.

A middle-aged worker, Pamela Livengood, began to speak, tentatively at first, about the drug addiction that has tormented her daughter and left her granddaughter in her care.

“This little 5-year-old lives with me, and I’m guardian — Grandpa and I have guardianship because of all the growing drug problems in our area,” Ms. Livengood said.

Mrs. Clinton gave her a sympathetic, knowing nod.

“Pam, what you just told me and what I’m hearing from a lot of different people, there is a hidden epidemic” of heroin, methamphetamine and prescription pills that is “striking in small towns and rural areas,” she said, taking out an index card and scribbling notes.