I ended up taking apart the carb to drain and clean it and letting the whole
rig dry overnight. I was able to get it started on the first pull after putting it all back together. I let it run about 10 minutes at a high throttle setting, but was having trouble keeping it running at idle. I suspect I may need to just adjust some of the carb settings to get it running smoothly again, but it seems to be none the worse for the wear. Time will tell.