If your rainy day fund is light, you have plenty of company. According to a newly released report from Bankrate, 24 percent of Americans have more credit card debt than emergency savings, and 13 percent are not much better off—they don't have credit card debt but they don't have emergency savings either. Put another way, more than a third of Americans are living at risk of a financial crisis.

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"Americans are woefully undersaved for emergencies," said Greg McBride, chief financial analyst at Bankrate. "By not having emergency savings and using some of your available credit, your options in the event of unplanned expenses are much more limited."

Generation X is the group shortest on emergency savings, Bankrate found, largely because they are in an expensive stage of life. Some 32 percent of respondents aged 30 to 49 had more credit card debt than emergency savings. "They've got the two kids, the dog, the car payments, the mortgage payments, the tuition payments," McBride said. "They are the poster children for stretched budgets." Read MoreAmerica's sorry savings

Millennials are in relatively better shape, with just 21 percent of respondents between 18 and 29 having more credit card debt than emergency savings. Perhaps that is because they have not hit the high-spending years and perhaps, as McBride said, "You are looking at a generation that had a front row seat for the financial crisis, so they have a greater tendency to save ingrained in them." Retirees were the most prepared for emergencies, with just 14 percent saying their credit card debt was bigger than their emergency savings.