Coaster brake takes a great deal of presure and then very little stopping ability even then. So what to do ? This off a cheap Japanese Schwinn. If that helps.
get the service manual for it and study it up. I think the sheldon brown site has it. shimano 333's are a pain, be gentle with the plastic bits, the grease doesn't seem to help them age any...
Chuck gave me one once. I took it part. It has a few more parts than the
nexus , but still didn't look too difficult to mess with. I took it apart and
put it back with nothing major happening .
if it is used , check for cracks on the middle of the hub , had a cracked coaster once , very hard to brake even with tone of pressure
if its new , maybe your gearing is to high you cant apply enough pressure