Think about the situation for a second. You'll be switching to other methods, and so will everyone else, all at once. Do Amex and Mastercard even have the capacity to take up the slack with no notice? Do you really think that every critical component of a cost-optimised system will have been over-provisioned to be able to take on hundreds of millions of additional customers in a single day? And if one fails, the demand switches to the remainder and crashes them too. It's a classic cascade failure.
I suspect it would take up the slack - depending on how the failure happened and when it happened.
I don't believe payment processors have the same number of payments every second, so Amex and MC have to be sized for the largest spike (+ some) that they can endure, and so unless Visa fell right when they were already maxed out, they'd likely continue.
And Visa has fallen before; if it was anything like a long-term failure, you know all the other processors would be spinning up as much extra capacity as they could. And many stores still have the paper machines for credit slips.
