Ryan,
That's your Throw out bearing. I'm pretty sure it shouldn't smoke. �Here is a photo of mine when I took it apart.


You may know all of this, but when you push on the clutch, it pulls the cable that is attached to the clutch fork. �The fork forces that throw out bearing against the 3 pressure plate fingers. �Those in turn release the pressure on the clutch plate and allow the engine to spin freely.
You throw out bearing could be shot. That might be why there is smoke. �Is the small spring still attached or broken? �If it's not attached, or broken, it won't pull the bearing back off the fingers.
What did the clutch feel like when you started having the problem?
Tim