Small Engines (Lawn Mowers, etc.): primer button, home mechanic, push mower

Question
I own a Murray push mower.  The other day I hit a rock so I had to replace the blade.  Lot of smoke came out when I hit the rock.  When I got it running again some more smoke came out.
  Then, it started konking out on me after a few minutes of running, and I noticed that the red rubber primer button was getting depressed (sucked in) while I was cutting the grass.  Every time (2-4 every minutes after starting it)I attempted to cut more grass....the button would suck in and it would cut the motor.
  Thank you for taking the time to read this.  cf

Answer
Hiya Charles

Your rock incident probably partially sheared the flywheel key, which sets the timing for the engine.  This unintended timing change will cause all the symptoms you mentioned.  The key is only about 4 bucks, but replacing it is tough for the home mechanic.  Wanna give it a shot?