I had the same problem with the Briggs and Stration engine on the mover.
Now then if you have the more modern mover it has an automatic choke, the carburetor is in the closed position for start up hence the engine needs to be primed. Once started a small flap attached to the fly wheel is pushed back with the draft of the motion, this then opens the carburetor via a butterfly device inside the carburetor. At the top of the carb there is a plastic stop for the automatic choke sometimes the mechanism gets stuck on top of the plastic and then the butterfly in the carb will not open hence very rich petrol mix and no air, result the engine will try to stall and then run. Here is the solution
There are three set screws holding down the rip cord mechanism take these out ( put in a container so as not to lose them) lift off the rip cord mechanism taking care
to make sure the oil dip stick is taken out, If you wish you can take off the oil stick by undoing the two small screws that hold it.
If you look down you will see the fly wheel and the flap that operates the choke gently move the flap away from the fly wheel if it is stiff to move then the mechanism at the top of the carb will be stuck and will not move easy if so gently move the mechanism over the plastic stop and then if done it will then go easy, job is now done.
baz
May 2010