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 Ms. 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. Ms. Mirzayans, a retired small-business owner, was grateful that the government was taking such interest in her insurance coverage.

Over glasses of pomegranate juice last month, Ms. 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 Ms. 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.”

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