The shopping cart is fluid and will try to adjust to the container. So it will adjust nicely on sidebars of different width but if your sidebar is too narrow then it won’t be able to fit properly. The width at least needs to be a size so the heading for each column (Item Name, Quantity, Price) can fit in one line otherwise the cart looks funny.
You can place the shopping cart on a separate page (For example: checkout page) if your sidebar is too narrow. Checking the following option in the eStore settings will make it so when someone adds a product to the cart it will automatically redirect to that page.
Automatic redirection to checkout page