LAFAYETTE, La. » Eight-year-old Draven Smith was expelled from school last year for disruptive behavior, and he is being expelled again this year. But his mother and his pediatrician cannot find a mental health specialist to treat him because he is on Medicaid, and the program, which provides health coverage for the poor, pays so little to doctors that many refuse to take its patients.

The problem is common here and across the country, especially as states, scrambling to balance their budgets, look for cuts in Medicaid, which is one of their biggest expenditures. And it presents the Obama administration with a major challenge, since the new federal health care law relies heavily on Medicaid to cover many people who now lack health insurance.

"Having a Medicaid card in no way assures access to care," said Dr. James B. Aiken, an emergency physician in New Orleans.

Nicole R. Dardeau, a 46-year-old nurse in Opelousas, La., in the heart of Cajun country, can attest to that. She said she could not work because of unbearable pain in her right arm. Doctors have found three herniated discs in her neck and recommended surgery, but she cannot find an orthopedic surgeon to take her as a Medicaid patient.

From her pocketbook, she pulls an insurance card issued by the Louisiana Department of Health and Hospitals.

"My Medicaid card is useless for me right now," Dardeau said over lunch. "It’s a useless piece of plastic. I can’t find an orthopedic surgeon or a pain management doctor who will accept Medicaid."

Medicaid, which is paid for jointly by the federal and state governments, is the subject of an intense debate in Washington over how to make it more efficient as Congress addresses the budget deficit and the growing national debt.

But for now the administration is counting on Medicaid to play a vital role in expanding access to health care under the legislation President Barack Obama signed into law just over a year ago. The program is already a major presence here, paying for 70 percent of births in Louisiana. State health officials estimate that the state Medicaid program will grow by more than 40 percent as a result of the federal health law, with the addition of 467,000 new recipients to 1.1 million now on the rolls.

"How can an already overtaxed Medicaid system handle such a huge influx of people?" asked Dr. Michael A. Felton, a family doctor in Church Point, La., near Lafayette.

It is a question being asked in many states. With the expansion of Medicaid to cover nearly all people under 65 with incomes up to 133 percent of the official poverty level (up to $29,330 a year for a family of four), Medicaid will soon be the nation’s largest insurer. It accounts for almost half of the increase in coverage expected under Obama’s health law but has received less attention than other parts of the law regulating private insurance.

The Congressional Budget Office predicts that average monthly Medicaid enrollment, now 56 million, will rise to 71 million by 2016, with another 5 million people added to the rolls in the five years after that.

Like many states, Louisiana has been struggling with a fiscal crisis. To hold down costs, it has cut Medicaid payments to doctors, dentists, hospitals and other health care providers several times in the past two years. Many providers report that the cuts, taken together, total 15 percent to 20 percent.

Louisiana officials said the cuts were necessary for two reasons: to avoid a budget deficit in the Medicaid program and to comply with a state law that limits Medicaid spending to the amounts appropriated by the State Legislature.

For patients like Draven Smith, whose mother said his behavior problems stemmed from attention-deficit hyperactivity disorder, the result is lack of access to doctors, especially specialists. For Draven’s pediatrician, Dr. Rachel Z. Chatters in Lake Charles, La., caring for poor children is a mission. About 80 percent of her patients are on Medicaid. It is, she said, painfully frustrating to beg and plead with other doctors to see Medicaid recipients.

"I devote one afternoon a week, every Wednesday afternoon, to trying to find specialists for my patients — a pulmonologist for children with chronic persistent asthma, a neurologist for children with seizures or developmental delays, a psychiatrist for children with serious mental health problems, a hematologist for patients with sickle cell disease," Chatters said.

Draven’s mother, Ana M. Smith, said: "I have tried for more than a year to find a child psychiatrist or psychologist to get Draven evaluated, but the mental health professionals in this area have told me they absolutely do not take Medicaid. If Draven could get the help he needs, I believe it would be unbelievably beneficial to him."

Some uninsured people will surely receive better care when they gain Medicaid coverage, doctors say. The new health law calls for a temporary two-year increase in Medicaid payments for some primary care services, but this does not affect specialists.

With the required expansion of Medicaid in 2014, Louisiana officials expect to enroll three groups of people: 260,000 newly eligible parents and childless adults; 20,000 parents now eligible but not enrolled; and 187,000 adults and children who drop private coverage and sign up for Medicaid.

Bruce D. Greenstein, secretary of the Louisiana Department of Health and Hospitals, acknowledged that "we have a hard time finding specialists for Medicaid enrollees."

Greenstein said the state expected to improve care and save money by enrolling most Medicaid recipients in managed care, an approach adopted by many states in recent years. In return for fixed monthly fees paid by the state, private health plans would coordinate the care of Medicaid patients, using networks of providers.

In passing the new health law, Congress wanted to make sure current Medicaid recipients would not lose coverage. Under the law, states generally cannot roll back Medicaid eligibility, but they can cut Medicaid in other ways — by reducing provider payment rates or by eliminating optional benefits.

About 20 states cut Medicaid payment rates for doctors last year, according to a survey by the Kaiser Family Foundation. At least 16 governors have proposed rate reductions this year for health care providers.

Gov. John Kitzhaber of Oregon, a Democrat, proposed cutting Medicaid payment rates for doctors, dentists, hospitals and nursing homes by 19 percent. Christine Miles, a spokeswoman for Kitzhaber, said his top priority was to preserve Medicaid eligibility for those who have it.

In Illinois, Gov. Pat Quinn, a Democrat, has proposed reducing Medicaid reimbursement rates by 6 percent for hospitals and nursing homes.

Gov. Brian Sandoval of Nevada, a Republican, has proposed cutting Medicaid rates by 5 percent for hospitals, 15 percent for nonprimary care doctors and 25 percent for dentists.

In South Dakota, Gov. Dennis Daugaard, a Republican, just signed a budget bill cutting Medicaid rates for doctors, dentists, hospitals and nursing homes — even primary care physicians and pediatricians.

In a few states, Medicaid recipients and providers have blocked cuts or secured higher reimbursement rates through litigation. But in many states, the promise of equal access remains unfulfilled.

Dr. Kim A. Hardey, an obstetrician-gynecologist in Lafayette, said he received about $1,000 from the Louisiana Medicaid program for providing prenatal care and delivery for a full-term pregnancy, compared with $2,400 from private insurance.

With the expansion of Medicaid eligibility, he said, more of his patients will be on Medicaid, and fewer will have private insurance, which helps offset the financial losses doctors sustain on their Medicaid business.

Already, Hardey said, many of his patients have jobs with private health insurance but switch to Medicaid when they become pregnant, thus avoiding premiums, deductibles and co-payments.