Brandon - broken bulb = no current flow = no possible chance of smell!
You may have an overheated plastic component in the top of one of the spotlight fittings or it could be a high resistance connection somewhere.
What often happens is that a securing screw only makes partial contact with the copper wire - perhaps it gets screwed down onto the plastic sheath and makes an adequate connection to begin with but only on a small area - a few sparks and a bit of soot build up and you get a high resistance connection. Anywhere where a screw bears onto a wire to make a connection is where you should check.
You will very probably (almost definitely) not see burnt cables. Blackened copper wire that should be shiny - or deformed and hot plastic parts maybe. You are looking for a bad connection at a terminal point - where the copper meets the thing it joins on to.
You are not pulling down the cables - you need to pull down the spotlights to examine their connections - the cables will be long enough to allow you to do this.
Try running just half the lights - see (smell) what happens - also examine the wall switch first- turn off power - remove switch plate - undo wires and inspect them - do it in a good light.
Peccavi
March 2009