The high shutter speed required so that the Sun doesn't wash out the whole photo doesn't let enough light in from the stars for them to be visible.

If you have a digital point-n-shoot camera, you can see this effect by trying to focus on the clouds while buildings and trees are also in the photo. If you focus on the clouds, the buildings/trees go dark because the camera restricts incoming light. If you focus on the buildings/trees the clouds become a blank white sky because the camera allows more incoming light, washing out the subtle differences between cloud and sky.

Stars are relatively very dim. To get a good shot of them, you'd have to make sure that the Sun and anything local that was reflecting sunlight was not in the frame. e.g. planets, moons, space stations, your hand.