A Cisco 7606 would not be used to limit upload size like that. It will be configure either for policing and traffic shaping. You can configure a burst size, but it is not likely to be related to this issue as the burst size would not normally be configured anywhere near this size.
My first guess - other users at the customer site using the circuit at the same time affecting the first user doing the upload.
My second guess is that the ISP is experiencing congestion towards You Tube.