Washington ? Every year, thousands of people make a deal with their doctor: I’ll pay you a fixed annual fee, whether or not I need your services, and in return you’ll see me the day I call, remember who I am and what ails me, and give me your undivided attention.

But this arrangement potentially poses a big threat to Medicare and to the new world of medical care envisioned under President Barack Obama’s health overhaul.

The spread of “concierge medicine,” where doctors limit their practice to patients who pay a fee of about $1,500 a year, could drive a wedge among the insured. Eventually, people unable to afford the retainer might find themselves stuck on a lower tier, facing less time with doctors and longer waits.

Medicare recipients, who account for a big share of patients in doctors’ offices, are the most vulnerable. The program’s financial troubles are causing doctors to reassess their participation. But the impact could be broader because primary care doctors are in short supply and the health law will bring in more than 30 million newly insured patients.

If concierge medicine goes beyond just a thriving niche, it could lead to a kind of insurance caste system.

“What we are looking at is the prospect of a more explicitly tiered system where people with money have a different kind of insurance relationship than most of the middle class, and where Medicare is no longer as universal as we would like it to be,” said John Rother, policy director for AARP.

Concierge doctors say they’re not out to exclude anyone, but are trying to recapture the personal connection shredded by modern medicine. Instead of juggling 2,000 or more patients, they can concentrate on a few hundred, stressing prevention and acting as advocates with specialists and hospitals.

“I don’t have to be looking at patient mix and how many are booked per hour,” said Dr. Lewis Weiner, a primary care physician in Providence, R.I., who’s been in a concierge practice since 2005.

“I get to know the individual,” Weiner said. “I see their color. I see their moods. I pick up changes in their lives, new stressors that I would not have found as easily before. It’s been a very positive shift.”

Making the switch can also be economically rewarding. If 500 patients pay $1,500 apiece, that’s gross revenue of $750,000 for the practice. Many concierge doctors also bill Medicare and private insurance for services not covered by their retainer.