If it is a feed of objects, then they do not go into the String constant pool unless you call intern(), as far as I know. The memory consumption for interned strings is not from the Heap, but from the Perm Gen memory space, so if you intern a lot of strings the application will crash with OutOfMemory, even if there is a lot of Heap left.
So it shouldn't be a concern unless you are interning all of these strings. If it becomes a concern, it would be possible to have your own Map implementation to store these strings, so you don't use the internal mechanism.
I checked the implementation of the intern() method and it is native, so it does not seem to be straightforward to measure the memory consumption, or to see the contents of the pool.
You can use this flag to increase the PermSize if you run out of memory:
-XX:MaxPermSize=64m