Sounds like the passageway is blocked. Two things to try... Tear down the carb completely removing everything that can be taken off. Put the carb into a container of carb dip, better than your regular carb cleaner. Good auto parts stores will carry it, usually in a metal can or jug. Let it soak a day or two to really let it work in.
Try blowing through the passages again. Still no flow? On to the next step... Get a big pot of water and put the carb in and boil the sucker. As you start to loose water from it boiling off add more water and get it back to a boil, just boil it for an hour or so.
If neither of these methods get that passageway clear then its time for a new carb. I find if carb dip won't break it up then its got some crap in it that the dip doesn't affect, maybe some dirt/rust that came down out of the tank, sometimes boiling will get enough heat in there and the water will help break it up, but not always.
I know a guy that uses an ultrasonic cleaning tank for stuff like this, wish i had one of those!
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1984 Honda ATC200ES "Big Red"
1982 ATC200E "Hondie"
1988 TRX300FW "Project Quad" Still in progress....