Cable companies don't hold the monopoly on video content anymore. This fact has been true for a while. The relatively new powerhouses that are YouTube, Hulu, Netflix, et al., have made sure of this.
Just like the distribution of print media has evolved beyond Gutenburg's scope, the same must happen for video. With so many developments occurring, it is a logical step for TV broadcasts to be surpassed. TV will eventually be killed off by the internet, but it will surely be a slow death. Cable companies will cling to their last breathes and hang on as long as they perceive themselves necessary, and audiences clinging to nostalgia will certainly aid in their losing battle. The same behavior is occurring right now with newspapers, who are still fighting for their place in the new world, a medium that has obviously outlived its usefulness.
For clarification of a misconception, when many speak of "the death of TV" they aren't actually referring to TV's at all, and sometimes not even what's appearing on the screen. The big issue is how that material is getting there. The television itself is going to stick around for a long time, longer than broadcast media will, it's just soon you won't be plugging a cable line into it, but instead will be hooking it up to a wireless network. This brings up another point why cable broadcast's death will be slow.
The fact is that sitting in front of a 16" computer monitor streaming compressed video isn't quite as gratifying as sitting in front of a big TV with broadcast quality images. High quality programming (in terms of picture quality, not content) is more readily available through cable, however there is a severe lack in variety, which the internet has. Once more interfaces are created for TVs to link to this internet content, people will be more willing to accept the change, so they can still sit in a daze on their couch.
The move to the internet also poses another problem: Piracy. The more access to material you grant to people on their own computers, the easier it is to steal it. It's harder to pirate content on a TV than it is on your computer. Anything that is streaming on Hulu or Netflix can be easily recorded on someone's computer with relatively unsophisticated software. This will obviously impede the transition.
Beyond that, another threat this poses to the internet is the death of the amateur videographer. Content generators will remain unaffected by the move to internet TV. Only their distribution changes, which means higher quality programming more widely available on the net. The innovation and creativity of amateur content generators, like users on YouTube, may become underplayed and ignored as people opt for professional work.
There are obvious positives that play in counterpoint to the above point. Advertising will gain the ability to become even more focused and cater to not only specific demographics but to specific individuals. Commercials and advertising on internet TV, like many ads on websites, will take into account personal information and statistics. This does pose some threat to privacy, but also now commercials will be actually directed at you. If you have to watch an ad, it is all the better if it interests you.
The whole idea of the internet helping regular TV is a mute point. Tweeting and posting about various shows have helped TV ratings, this is true. But when internet TV picks up speed there will be no reason to cross platforms. Now, someone sees a tweet and they turn on their TV, soon, when a person reads a Tweet about a show they'll just have to check it out online. This closed system will further help separate regular TV broadcast from the internet, striking a blow to cable TV in the long run.
Here's the best part of all this: You'll be able to enjoy the same exact content as before, have access to more content, and you won't have to deal with (or pay) for content you don't want.