The camera is working pretty hard to do video (saving it to the camera's memory); you could upload the video and stream it, but not in real time (ie live). A still camera is just too busy to output the video in real time.
I suppose it's not impossible, but the camera would have to be designed specifically to output to the USB port in real time. If you run across one that claims to work that way (even if it's only via Windows) then you could probably use a driver from IOXperts to get it on the web. But it's not a normally offered feature of a still digicam.