There are two options for trading off quality: you can show smaller frames or fewer frames. It looks like people have done both. These are both technically "Narrow Band Television", but generally the former gets this name and the latter is called "Slow Scan Television". Narrow band is how television started, with very small pictures at full speed. SSTV is more recent, being used by ham radio operators to send primarily still pictures. Both of these are within reach of a sound card and can be done.

For hooking a computer up to a modern but analogue television, SSTV would definitely not work for several reasons. The biggest is that the phosphor on the tv needs to be refreshed very often, and at several seconds a frame the top half of the screen would be long dark by the time the bottom half was drawn. It also seems that while the NTSC format does say the TV needs to sync up to the video input signal, that's mostly for fine correction. Sending the sync signals at a speed 1/150th or so of what was expected by the TV designers is unlikely to work.

Narrow band TV is also not likely to work, but has a greater chance of working. If we can send the syncs proprly, we ought to be able to get it to jump back to the top of the screen after only sending 15 lines or so. This would let us draw a small image, though it would be way stretched. The problem, I think, is that we would need to send the sync signals with greater resolution than we can manage with a sound card.

Update: 2009-11-26. Blake writes to give a link to using a vga card to generate DVB-T signals. Unlike an audio signal, a vga signal does have high enough bandwidth to display proper images. You need a card that can do 4096x2048 at exactly 76.5 MHz. Hmm.