Thanks Rob, we are further ahead - we have confirmed that the problem is lean mixture, probably due to gum in the Walbro carburetor. (We also need to consider the possibility that the gasket between the carburetor and inlet port is damaged, creating a vacuum leak.) If you look at the illustrated parts list, you will see that Item No. 127 is a welch plug that is driven in below the main jet, and holds it in place. To remove the main jet it is necessary to prise out the welch plug, which will be trashed by that process and you would have to get another one to keep your main jet from dropping down out of position. Before we attack the carburetor though, I have to ask whether your carburetor has an anti-afterfire solenoid screwed to the bottom of the float bowl? I can't tell from your photo, the view doesn't go down that far. The version of the carburetor without the solenoid just has a metal screw at the bottom center of the float bowl, holding it on. The version with the solenoid has a black cylindrical object there instead of the metal screw. A wire attaches to the black object. If you have a solenoid, that may well be the source of the problem since they are prone to giving trouble.

Here is the version without the solenoid:
[Linked Image]

Here is the one with the solenoid:
[Linked Image]

Those pics are cut from a set of internet instructions for cleaning an early version of your carburetor, before the welch plug was added as an anti-tampering measure:
http://outdoorpowerinfo.com/repairs/briggs_walbro_lmt_carb.asp

Check whether you actually have a welch plug. If you do not, just follow those instructions for cleaning. If you do, we can talk about a partial cleaning that should do the job without requiring a new welch plug.