Doctor visits are being given away at this year’s State Fair as freely as backpacks and yardsticks. Not on a stick, mind you, but online.

Blue Cross and Blue Shield of Minnesota has handed out 4,000 vouchers so far for e-visits with doctors through a website called Online Care Anywhere.

The timing of the marketing campaign might seem odd in that Online Care has been treating patients remotely for three years.

But in many ways, the giveaway is perfectly timed.

Early next year, when federal health reform expands the number of Minnesotans with health insurance by the thousands, there could be a shortage of face-to-face appointments with doctors.

That happened after Massachusetts’ expansion of health insurance in 2006. So online care could become a hot commodity.

“All of a sudden, we will likely have a huge new pool of patients looking for physicians, no question,” said Dr. Peter Antall, a California pediatrician.

He is medical director for American Well, the company that links patients via the Online Care website to a national network of doctors.

Blue Cross was an early innovator with American Well in 2009, when it invited employees at its Eagan office to visit doctors online. Now Online Care is available to 30 million people in 21 states, for fevers, pinkeye and more.

Patients interact with doctors via webcams, often after hours, when local doctors and urgent care clinics aren’t available.

Antall’s network includes doctors in other states who are licensed in Minnesota.

(When I checked, family medicine specialists from Plainfield, Ill., and Frisco, Colo., were available.)

Initial concerns about matching Southern patients to docs with Boston accents turned out not to matter. Patients place higher value, Antall says, on timely care from doctors they trust. “A good doctor is a good doctor,” he said.

Antall expects some patients will bring marginal health problems to the site just to take advantage of the fair freebie, which expires Nov. 30.

“Part of our strategy is just to keep reminding patients that this does exist,” he said, “that we can do a lot of things and take care of a lot of conditions.”