Are you having trouble finding a doctor who will see you? If not, give it another year and a half. A doctor shortage is on its way.

Most provisions of the Obama health law kick in on Jan. 1, 2014. Within the decade after that, an additional 30 million people are expected to acquire health plans—and if the economic studies are correct, they will try to double their use of the health-care system.

Meanwhile, the administration never seems to tire of reminding seniors that they are entitled to a free annual checkup. Its new campaign is focused on women. Thanks to health reform, they are being told, they will have access to free breast and pelvic exams and even free contraceptives. Once ObamaCare fully takes effect, all of us will be entitled to a long list of preventive services—with no deductible or copayment.

Here is the problem: The health-care system can’t possibly deliver on the huge increase in demand for primary-care services. The original ObamaCare bill actually had a line item for increased doctor training. But this provision was zeroed out before passage, probably to keep down the cost of health reform. The result will be gridlock.

Take preventive care. ObamaCare says that health insurance must cover the tests and procedures recommended by the U.S. Preventive Services Task Force. What would that involve? In the American Journal of Public Health (2003), scholars at Duke University calculated that arranging for and counseling patients about all those screenings would require 1,773 hours of the average primary-care physician’s time each year, or 7.4 hours per working day.

And all of this time is time spent searching for problems and talking about the search. If the screenings turn up a real problem, there will have to be more testing and more counseling. Bottom line: To meet the promise of free preventive care nationwide, every family doctor in America would have to work full-time delivering it, leaving no time for all the other things they need to do.

When demand exceeds supply in a normal market, the price rises until it reaches a market-clearing level. But in this country, as in other developed nations, Americans do not primarily pay for care with their own money. They pay with time.

How long does it take you on the phone to make an appointment to see a doctor? How many days do you have to wait before she can see you? How long does it take to get to the doctor’s office? Once there, how long do you have to wait before being seen? These are all non-price barriers to care, and there is substantial evidence that they are more important in deterring care than the fee the doctor charges, even for low-income patients.

For example, the average wait to see a new family doctor in this country is just under three weeks, according to a 2009 survey by medical consultancy Merritt Hawkins. But in Boston, Mass.—which enacted a law under Gov. Mitt Romney that established near-universal coverage—the wait is about two months.

When people cannot find a primary-care physician who will see them in a reasonable length of time, all too often they go to hospital emergency rooms. Yet a 2007 study of California in the Annals of Emergency Medicine showed that up to 20% of the patients who entered an emergency room left without ever seeing a doctor, because they got tired of waiting. Be prepared for that situation to get worse.

When demand exceeds supply, doctors have a great deal of flexibility about who they see and when they see them. Not surprisingly, they tend to see those patients first who pay the highest fees. A New York Times survey of dermatologists in 2008 for example, found an extensive two-tiered system. For patients in need of services covered by Medicare, the typical wait to see a doctor was two or three weeks, and the appointments were made by answering machine.

However, for Botox and other treatments not covered by Medicare (and for which patients pay the market price out of pocket), appointments to see those same doctors were often available on the same day, and they were made by live receptionists.

As physicians increasingly have to allocate their time, patients in plans that pay below-market prices will likely wait longest. Those patients will be the elderly and the disabled on Medicare, low-income families on Medicaid, and (if the Massachusetts model is followed) people with subsidized insurance acquired in ObamaCare’s newly created health insurance exchanges.

Their wait will only become longer as more and more Americans turn to concierge medicine for their care. Although the model differs from region to region and doctor to doctor, concierge medicine basically means that patients pay doctors to be their agents, rather than the agents of third-party-payers such as insurance companies or government bureaucracies.

For a fee of roughly $1,500 to $2,000, for example, a Medicare patient can form a new relationship with a doctor. This usually includes same day or next-day appointments. It also usually means that patients can talk with their physicians by telephone and email. The physician helps the patient obtain tests, make appointments with specialists and in other ways negotiate an increasingly bureaucratic health-care system.

Here is the problem. A typical primary-care physician has about 2,500 patients (according to a 2009 study by the Centers for Disease Control and Prevention), but when he opens a concierge practice, he’ll typically take about 500 patients with him (according to MDVIP, the largest organization of concierge doctors): That’s about all he can handle, given the extra time and attention those patients are going to expect. But the 2,000 patients left behind now must find another physician. So in general, as concierge care grows, the strain on the rest of the system will become greater.

I predict that in the next several years concierge medicine will grow rapidly, and every senior who can afford one will have a concierge doctor. A lot of non-seniors will as well. We will quickly evolve into a two-tiered health-care system, with those who can afford it getting more care and better care.

In the meantime, the most vulnerable populations will have less access to care than they had before ObamaCare became law.