The computer industry will certainly push for higher resolution panels, mostly because ~200 dpi allows for vastly better text rendering. I tend to think that the technology will be in place for reasonably priced consumer 4K within the next four years or so, but that there really won't just be much consumer demand. You have to sit almost comically close to a 50" TV before you start wishing you had more detail than 1080p provides. Consumer 4K stands a good chance of ending up like SACD and DVD Audio; most people thought CDs were more than good enough, so these formats went nowhere. In fact, the formats that eventually did largely replace the CD -- MP3 and AAC -- were lower quality, but more convenient.
Maybe if TVs keep getting bigger... but I think they may already be large enough that most people don't really want something bigger in their living rooms, so there might have to be some big change in technology for that to happen. ("Screen paint" that turns walls into screens or something. Give it 20 years.)
Maybe I'm wrong about all this, and consumer 4K will be the big summer hit of 2014. But I suspect if Red wants to make a play for the mainstream consumer distribution market, what they should do is develop a version of the RedRay codec optimized for 1080p Internet streaming. If what happened with music is any guide, Blu-ray won't be replaced by a higher quality physical media format, but by a substantially more convenient (and possibly somewhat lower quality) downloadable and streamable format.