Rep. Mark Meadows, North Carolina Republican, recently introduced bill that would limit initial opioid prescriptions for acute pain to seven days, except in cases of traumatic injury, chronic conditions or a doctor’s specific recommendation.

“Most addictions start after the seventh day. And a lot of times when physicians do a surgery, they just do a 30-day prescription,” Mr. Meadows said.

Those remaining 21 days are a concern, since too many Americans unwittingly get hooked on prescription opioids and — in some cases — later turn to cheaper heroin.