Available evidence suggests that the average marginal propensity to consume (MPC) from the 2001 tax rebate in the US was not nearly as large as that from previous tax cuts. We examine if this phenomenon can be explained by the fact that the widespread use of credit cards has made borrowing accessible for most US households by constructing a model that simulates the dynamic effect of relaxed borrowing constraints. Our model uses Kreps-Porteus preferences which account for independent measures of relative risk aversion and the elasticity of intertemporal substitution, both of which can theoretically affect the willingness to save or spend. Our model shows that the average MPC drops substantially immediately after borrowing constraints are relaxed because few consumers have binding borrowing constraints at that time. The model also shows that consumers gradually reduce their wealth after borrowing constraints are relaxed, causing more of them to have binding constraints over time, which in turn causes the average MPC to rise gradually to a new steady state value that is slightly lower than the original value. This dynamic pattern of the MPC suggests that a greater ability to borrow with credit cards could explain the lower effectiveness of the 2001 tax rebate. In addition, the model predicts that consumers choose to hold lower amounts of liquid assets for precautionary reasons when they have a greater ability to borrow unsecured debt.