For many Americans, a single unplanned expense could set them in a tailspin. Worse yet, those who will likely need a rainy-day fund the most are also the least prepared.

When broken down by age, young boomers fared the worst: Nearly one-third, or 32 percent, of those ages 53 to 62 said they had zero dollars saved in an emergency fund, compared with 24 percent of all others ages 18 or older, according to a Bankrate.com survey of 1,000 adults conducted this month. (Older boomers — over age 63 — were much more likely to have something set aside.)

Generally, the likelihood of having saved at least six months of expenses increases steadily with age, Bankrate said. Yet for younger boomers, "it's a reflection of prolonged unemployment in the years following the financial crisis," said Greg McBride, Bankrate's chief financial analyst.

And for this generation, facing the very real possibility of increased medical expenses in the near term, an unplanned bill can come at a severe cost.