This paper addresses the credit card debt puzzle using a generalization of the buffer‐stock consumption model with long‐term revolving debt contracts. Closely resembling actual US credit card law, we assume that card issuers can always deny their cardholders access to new debt, but that they cannot demand immediate repayment of the outstanding balance. Hereby, current debt can potentially soften a household's borrowing constraint in future periods, and thus provides extra liquidity. We show that for some intermediate values of liquid net worth it is indeed optimal for households to simultaneously hold positive gross debt and positive gross assets even though the interest rate on the debt is much higher than the return rate on the assets. Including a risk of being excluded from new borrowing which is positively correlated with unemployment, we are able to simultaneously explain a substantial share of the observed borrower‐saver group and match a broad range of percentiles from the empirical distributions of credit card debt and liquid assets.