Pictures would help.
Are you using a bottoming tap where the cutting threads go all the way to the end?
Cutting the threads with a tap is easy. If the hole is not deep enough so that a normal tap did not cut threads to a length the same as the stopper, I can imagine it to be difficult to get the stopper mounted.
I normally do not have a problem getting the the stopper into the threaded hole.
You could try 11/32in dia drill bit.
Are you using a bottoming tap where the cutting threads go all the way to the end?
Cutting the threads with a tap is easy. If the hole is not deep enough so that a normal tap did not cut threads to a length the same as the stopper, I can imagine it to be difficult to get the stopper mounted.
I normally do not have a problem getting the the stopper into the threaded hole.
You could try 11/32in dia drill bit.