Cal,
You need to explain exactly what happened.
What you heard, felt, smelt & saw.
When a pulley jambs oft you get a burnout on the belt at the engine pulley.
In that case the belt gets too thin in one spot to drive, so you go nowhere.
Very rare to damage the pulley to the point it won't drive at all.
Very easy to get the belt on the wrong side of a belt keeper, particularly on that back pulley.
The mower was running and cutting fine til I hit the small branch (didn't notice til too late). Shortly after the mower felt and sounded "rough". I stopped to look at it and at first did not see anything until I tried to go again and it didn't. Upon further inspection I noticed the branch wedged around the pulley (between the pulley and belt). I removed it but it did not rectify the issue. I am taking off the wheels to see what else could be wrong. I am just trying to nail down a starting point.