Health savings accounts are unlikely to be much help to retirees, according to the Employee Benefit Research Institute. Instead, statutory contribution limits mean retirees will fall short of the savings needed to fund their health care.

According to EBRI's analysis, if a 55-year-old worker contributed $3,000 to an HSA in 2009, and contributed the maximum annual catch-up of $1,000 for 10 years, the account would have $48,300 assuming a 2 percent interest rate. However, it's estimated that a 55-year-old man today will need between $144,000 and $290,000 in 2019, just to have a 50 percent chance of covering premiums and out-of-pocket expenses for Medigap and Medicare Part D.

"One of the difficulties in using an HSA to save money for premiums and out-of-pocket expenses during retirement is that contributions to the HSA are limited by law; and as a result, the savings needed for retiree health care far exceed the savings potential of an HSA," according to the analysis. "Furthermore, individuals can (and may need to) use the money in the account to pay for health care services during their working years or to pay COBRA premiums and insurance premiums during periods of unemployment."