Try this as a quick fix, tie the brake cable start the mower and keep on pushing the primer bulb to keep the engine running this should clean out all of the old gas out of the carb make sure you have fresh gas in the tank, hope you did not have 1/2 tank of old gas and you just added fresh gas. when I say fresh gas I mean fresh no more then a few days old and the tank must have all fresh. If this fails let me know and we will go to the next step

Sounds like a Tecumseh problem, not a Briggs! Are you sure of the engine mfgr?
Rustyj

On the bottom of the carb, the bowl is held on with a brass "nut".
That is the carb Main Jet.
Clamp off the fuel line, remove the jet and clean the holes with a fine wire like you'd finf on the tie for a loaf of bread.
Flush the fuel line for a couple seconds, re-clamp and install the part.
You should be good to go.

I have a similiar problem with a Craftsmans edger. You say that the bowl is held on with a brass nut. Is this the float bowl? It is held on to the carb by a brass "High speed bowl nut" and screws into "Main nozzle tube". Do I clean out both the "high speed bowl nut" and "main nozlle tube" with the wire?

Any help would be appricated.