WASHINGTON — Alarmed by a shortage of primary care doctors, Obama administration officials are recruiting a team of "mystery shoppers" to pose as patients, call doctors' offices and request appointments to see how difficult it is for people to get care when they need it.

The administration says the survey will address a "critical public policy problem": the increasing shortage of primary care doctors, including specialists in internal medicine and family practice. It will also try to discover whether doctors are accepting patients with private insurance while turning away those in government health programs that pay lower reimbursement rates.

Federal officials predict that more than 30 million Americans will gain coverage under the health care law passed last year. "These newly insured Americans will need to seek out new primary care physicians, further exacerbating the already growing problem of PCP shortages in the United States," the Department of Health and Human Services said in a description of the project that it submitted to the White House.

Plans for the survey have riled many doctors because the secret shoppers will not identify themselves as working for the government.

"I don't like the idea of the government snooping," said Dr. Raymond Scalettar, an internist in Washington. "It's a pernicious practice — Big Brother tactics, which should be opposed."

According to government documents obtained from Obama administration officials, the mystery shoppers will call medical practices and ask if doctors are accepting new patients and, if so, how long the wait would be. The government is eager to know whether doctors give different answers to callers depending on whether they have public insurance, like Medicaid, or private insurance, like Blue Cross and Blue Shield.

Dr. Robert L. Hogue, a family physician in Brownwood, Texas, asked: "Is this a good use of tax money? Probably not. Everybody with a brain knows we do not have enough doctors."

In response to the drumbeat of criticism, a federal health official said doctors did not need to worry because the data would be kept confidential.

Administration officials said the survey would yield an enormous benefit to the government while imposing an extremely limited burden on doctors.

Federal officials said the initial survey would cost $347,370. Hogue said the money could be better spent on the training or reimbursement of primary care doctors.