After a phased start-up, the city plans to bring private medical networks into the program next year, expanding the choice of doctors. Until November, enrollment will be limited to those living below the federal poverty line ($10,210 for a single person; $20,650 for a family of four). Then it will open to any resident who has been uninsured for at least 90 days, regardless of income or immigration status.

Only then will city officials learn whether the program appeals to middle-class workers, who comprise a growing share of the uninsured. And only then can they test whether San Francisco has the medical infrastructure to handle the desired increase in demand, and to do so without raising taxes. So far, enrollment has exceeded expectations. The city projected that between 600 and 1,000 people would sign up by the end of August. More than 1,300 did, even though officials have done little marketing. They hope to enroll about 45,000 people — more than half of the city’s uninsured — in the first year. Some clinics are adding night hours and small numbers of staff.

“We really didn’t know what the interest level would be so we’ve very pleased,” said Mayor Gavin Newsom. “At the same time, we don’t want over-exuberance yet because we don’t want to fall of our own weight.”

At the two pilot clinics, efforts are first made to qualify patients for Medicaid or other state and federal insurance programs. Those left over receive a Healthy San Francisco card that makes them eligible for primary care, dental exams, mental health and substance abuse services, hospitalization, radiology and prescription drugs.

Because the coverage is not portable, officials believe that those with private insurance will have little incentive to drop their policies to take advantage of the city’s cut-rate services.

Like Ms. Ho, many of those enrolling were already using the city’s health clinics — or the emergency room at San Francisco General Hospital — in times of acute need, like an asthma attack or stroke. About 57,000 of the 82,000 uninsured San Franciscans have used the city’s health system at some point.

But the new program hopes to persuade them to become regulars who regard their neighborhood clinic as a medical home. Once enrolled, patients are assigned a physician and encouraged to get blood pressure checks, mammograms and other screenings.