WYCKOFF, N.J.—An hour wait at the MinuteClinic?

That was the scenario one morning last week as prospective patients sat slumped in chairs, waiting for medical care at the back of a modest CVS drugstore in a strip mall here in suburban New Jersey. Urinary-tract infections, the flu, ringworm, diabetes screening, earwax removal, pinkeye, and many a sore throat and cough—they came for it all.

"The wait time is too long, I'll come back later," said one woman after seeing a greater-than-two-hour estimate on the touch-screen kiosk where patients sign in. Mary McCormack, a nurse practitioner for MinuteClinic, said the wait time on the kiosk was inaccurate since they had two practitioners that day.

"I don't think that thing is so very far off," chimed in patient Nancy Tanner, in between coughing. "I've been here 45 minutes." Still, the 62-year-old said it's better than the rigmarole of making an appointment at the doctor's office, where the wait would be just as long even with an appointment.

Currently there are about 1,600 walk-in medical clinics across the country in drug and big-box stores and supermarkets like CVS, Walgreens , Target and Kroger. The number is projected to double in the next three years due in part to the increased demands of newly insured patients under the Affordable Care Act, according to a 2013 report from Accenture, a global management-consulting firm.