Sebelius has insisted that the company justify the rate increase in detail to her agency. "We need to make sure that companies are spending their money on health claims, not on overhead costs," she added.
Fluegal, though, says insurance company profits are not really the key factor driving health care cost increases. He said the bigger issue is the need to better control medical costs.
Some critics point out that insurance companies are canceling costs by canceling sick peoples' policies.
Asked whether Anthem would be willing work out payment plans with customers who couldn't afford the rate increases, Fluegal replied: "Well, we would encourage people … to give us a call."
Libresco did just that, and an Anthem representative directed him to a different plan that could save him $90 a month, but that plan decreases the number of doctors' visits and increases prescription costs.
ABC News' Jake Tapper and The Associated Press contributed to this report.