What happens if my area is right on 13 x 13 feet or slightly smaller, when using PS Eye cams?

Basically, the capture area (where an actor is fully visible to all cameras) will be pretty small. You can move in a wider area, so an actor is only partially visible in some of the cameras, but this may lead to a geater number of tracking errors.
One of users shares his experience of setting up a small room for capturing with PS Eyes in this topic:
http://forum.ipisoft.com/viewtopic.php?f=2&t=9004

Sounds like he didn't have any issues.

You can try to connect with this user directly to discuss his experience in more detail.
I just state that we recommend rooms of greater size for capture with PS Eyes to unleash the full potential of PS Eye setup and to avoid possible problems.