To the list of problems plaguing President Barack Obama’s health care law, add one more – fraud.

With millions of Americans frustrated and bewildered by the trouble-prone federal website for health insurance, con men and unscrupulous marketers are seizing their chance. State and federal authorities report a rising number of consumer complaints, ranging from deceptive sales practices to identity theft, linked to the Affordable Care Act.

Madeleine Mirzayans was fooled when a man posing as a government official knocked on her door. Barbara Miller and Maevis Ethan were pitched by telemarketers who claimed to work for Medicaid. And Buford Price was almost ensnared by another new trap: websites that look official but are actually bait set by fly-by-night insurance operators.

Some level of fraud or abuse is predictable with any big government program, and administration officials expected a few bad actors to emerge. Attorney General Eric H. Holder Jr.; Kathleen Sebelius, the secretary of health and human services; Edith Ramirez, the head of the Federal Trade Commission; and other officials met at the White House in September to discuss possible pitfalls.

But now the technical failures troubling the HealthCare.gov website, as well as the law’s complexity, threaten to make matters worse. Only a tiny fraction of Americans have been affected so far, but state authorities and the FTC are reviewing the issue aggressively.

"With this changing health insurance landscape, there is a new opportunity for people to take advantage of our residents, and we’ve seen it starting already," said Kate Abernathy, a spokeswoman at the Tennessee Department of Commerce and Insurance.

While it is difficult to quantify the problem, interviews with authorities in states including California, Florida, Illinois and New York suggest that fraud is a growing worry. Websites are particularly difficult to police.

"We are remaining vigilant, since we anticipated that the law was so complex that scam artists would take advantage of it," said Tom Miller, the attorney general of Iowa. In New York and Illinois, attorneys general are investigating at least two firms that they suspect of fraud, according to people briefed on the matter. Since October, attorney general offices in 36 states have been holding conference calls about the emerging dangers every two weeks.

The most prevalent complaints involve older Americans. Under the law, people age 65 and over, who are on Medicare, do not need to buy supplemental coverage. Nonetheless, some marketers are pushing expensive add-on policies by falsely claiming that such coverage is required, state authorities say. Others are telling people that the law means they need new Medicare cards – not true. And still others are charging fees as high as $100 to "help" people navigate the new insurance landscape.

Then there are those who are creating websites that resemble state health care exchanges. Visitors to those websites, with addresses like "NewHampshireHealthExchange.com," say they are inundated with pitches from private insurance agents unaffiliated with the government.

Authorities warn that in some cases the come-ons are merely a ruse to get people to divulge sensitive Medicare and banking information. The pitches usually come with a telephone call or knock at the door. Someone claiming to be a government official offers help or warns residents that their Medicare cards are about to expire. Then the hook is set.

To Mirzayans, 68, the caller sounded so official that she agreed to meet him the next day at her home in Sherman Oaks, Calif. He told her the law meant she would have to update her Medicare card. Mirzayans, a retired small-business owner, was grateful that the government was taking such interest in her insurance coverage.

Mirzayans divulged to her visitor crucial Medicare, Social Security and personal information. Only after the man left without giving her a business card did she grow suspicious.

"I just feel so foolish and betrayed," said Mirzayans, who reported the incident to state authorities.

She is hardly alone. Across the country, volunteers with Senior Medicare Patrol, a government program that works with older Americans to root out health care fraud, say they have been deluged with calls for assistance. The typical complaints are from retirees who said they had handed over bank account information to callers claiming to be from Medicare.

Anne Gray, a project coordinator in California with the Senior Medicare Patrol, said, "Such calls have doubled in recent months."

Miller and Ethan, both of whom live in California, said they had also received calls from people urging them to update their Medicare cards in light of the new law. Neither fell for the ploy.

In Kentucky, Elsie Burdon, 70, said she knew she had slipped up almost as soon as she hung up the phone. She had divulged her Medicare information and Social Security number. Burdon, of Jenkins, Ky., said the caller assured her that Medicare was changing, inquired about her diabetes and even asked about her shoe size.

"I thought it was odd," Burdon said, adding that she had immediately contacted her bank and state authorities. Days later, she got a flood of other marketing calls. "I can’t even keep track," she said. "First it was a Joe, then an Ashley and then at least six other people all claiming to be from the government."

Anyone, young or old, can be targeted by the unscrupulous marketers. But older people – whether because of age, their tendency to be at home often or other factors – are particularly vulnerable. Medicare has also long been a magnet for swindlers, thanks to its sheer scale and complexity. The troubled rollout of the new health care law has amplified the problem.

"The scammers are deploying traditional Medicare cons but wrapping them in the Affordable Health Care Act," said James Quiggle of the Coalition Against Insurance Fraud, a Washington-based nonprofit.

With all the problems surrounding the federal websites, it can be even more difficult for consumers to navigate. In October, New Hampshire’s insurance commissioner hit the operator of "NewHampshireHealthExchange.com," an insurance provider in Arizona, with a cease-and-desist order.

Lisa Madigan, the Illinois attorney general, is investigating a website over concerns that it is a lead generator for insurance providers not registered to do business within the state, the people briefed said.

Price, 75, who lives in Willis, Texas, concedes that he is not technology-proficient. "I don’t do the Internet," he said. But he was surprised at how quickly a wrong turn on the web had led to a barrage of marketing calls. While he and a friend were watching football one recent Sunday, the friend entered Price’s name and phone number into a pop-up window that appeared when Price was on an official-looking government website. Roughly five minutes later, Price said, his cellphone rang.

On the line, Price said, was a man who offered to come by his house the next day. Price declined – but got three more calls later that week.

"I know the Internet is fast," Price said, "but this was something else."