The current Oculus Dev kit is only 1280x760 and not a full 1080p display (I have one), what this leads to is 640x760 per eye which is the equivalent of playing a game back in the early 1990's.
I believe the HD version of the Oculus that they showed off at E3 this year was a full 1920x1080 giving each eye 960 x 1080.
Most 4K TVs operate at 3840x2160 which would give 1920 x 2160, this is roughly 10x as many pixels in the current Dev Kit.
Going to 4K would really help for games that are attempting to look more realistic, as well as increase viewing depth in the 3D environment. Packing this many more pixels into the same physical space should also resolve issues with the screen door effect we currently see with the Oculus Rift Dev kit where you can see between the pixels.
The only issue that I see with a 4K screen is that the graphics cards that can support a 4K environment would be pretty high and would limit the number of users that could afford to use a Rift. Also increasing the pixel count will increase the rendering time, and this will add to the latency between what a person see's, how they move, and how that movement impacts their view of the rendered environment. The longer this takes, the greater chance there is a delayed drag effect to the motion. You move your head, and the view has to catch up to you like you are dragging the view.
I look forward to buying future Oculus hardware, I like the dev kit, it shows a ton of promise, but they have a long way to go.