There are three main aspects regarding TV reception: Receiving, decoding, and output.
In the past, the most critical part was imho output, and it still is: Only very few solutions exist that allow to create interlaced PAL TV output without scaling and messing up the field order.
For the HDTV future, this will be different. In the past, a TV output was some kind of attachment to the graphics card. Now, since HDMI is compatible to DVI, a primary DVI output is the best solution to connect a HDTV display. Its just a matter of time until modern graphics cards will be able to produce fully HDTV compatible output for TV sets, including audio.
Next thing is decoding. HDTV will soon be directly related to MPEG4/AVC, to keep bandwidth in an acceptable range. For the main CPU, this is still a difficult task, so hardware accelerated decoding should be the path. My guess is that most next generation graphics cards will have MPEG4/AVC and VC-1 decoders built in. Getting this on Linux will take some time, but its not impossible.
Finally, reception. This sounds like the easiest part, but I fear that this will be the one that stops us. With the current attitude of the movie and TV industry, we'll probably get HDTV only in DRM'ed versions, so they can force their no-recording dreams on us. I don't see that they allow open source software to access the video streams, just like they never allowed open source software for CSS protected DVDs. And my guess is that this time it wont be that easy to get around it.
Basically, I think the future lies in budget cards combined with hardware accelerated graphics cards for output. However, there's no point in wasting time on this topic until we know for sure that there will be open access to the video stream, and it doesn't look like that in the moment.
Cheers,
Udo