The stumbling would more likely be a firing issue like dirty plugs or something with the coil. Not so much fuel delivery BUT that doesn't mean you should rule it out. You could try pulling a few plugs and if their overly fouled you could replace em or clean them up. And i shouldn't have to suggest this and i assume you do have an air filter on there :P Unless bits of that got sucked in nothing big enough to cause an issue should get by. If you can get it to a point of stumbling all the time take a test light and wrap a unfolded paper clip on the end, then ground it. Stick the paper clip into the boot of each plug wire on the cap and whichever plug shorts out and doesn't change the motors stumbling would be a bad plug/wire/contact on the cap. I doubt that is the issue though.

And one more thing, if you got any carb cleaner laying about, spray it into the carb and run it and see if it helps. It may be gummed up.