Oh yes it could be the clutch! Overloading the driveline could cause the clutch to slip and that smells a bit like burning rubber. And if you were stationary, you slipped the clutch to start that tire spinning, right?
How much damage can it do? If you can smell it, then you just rubbed, say, $10 off the tire. Do that enough and the tire explodes. Keep in mind, because of the differential. if ONE tire is spinning and the other is not, the spinning tire’s speed is double what shows on the speedometer.
See the discussion and @B.L.E 's post here;