The data is highly compressed, so it watching a one hour show would consume considerably less bandwidth than the 800MB-3.6GB digital file that a TiVo may store the program in, depending on quality. It is still bandwidth intensive though, and generally reqires 3G or higher speeds to work properly.
The potential data usage has apparently become a point of concern for AT&T, so they have bocked the service over its 3G network. They cite their terms of service as the reason for the block. "...but downloading movies using P2P file sharing services, redirecting television signals for viewing on Personal Computers...is prohibited." Technically, your phone isn't a personal computer, but AT&T disagrees.
Engadget has the full AT&T statement on the matter, but here are the key statements:
Slingbox, which would use large amounts of wireless network capacity, could create congestion and potentially prevent other customers from using the network. The application does not run on our 3G wireless network. Applications like this, which redirect a TV signal to a personal computer, are specifically prohibited under our terms of service. We consider smartphones like the iPhone to be personal computers in that they have the same hardware and software attributes as PCs.
That said, we don't restrict users from going to a Web site that lets them view videos. But what our terms and conditions prohibit is the transferring, or slinging, of a TV signal to their personal computer or smartphone.
I am having trouble seeing the difference from watching a video from a webserver and watching a video from your house. AT&T touts the 3G network as a "powerful 3G mobile broadband network." It just isn't powerful enough to sling TV shows around.