A $2,000 purchase does not stay a $2,000 purchase once credit card interest starts piling up. With credit card rates hovering around the 24% range for some borrowers and balances, carrying that charge for months can add hundreds of dollars to the price.
That makes the real question less about whether the card has enough available credit and more about how long the balance will remain there. A purchase that fits comfortably into a monthly budget can become considerably more expensive if the repayment plan stretches out.