I think of this in the following context: when someone tries to be everything to everyone, they end up being nothing to nobody. That of course is a double negative, but I believe expresses the intent of what I am looking for very well. That is, you end up being the opposite of everything to everyone. Can anyone think of a opposite that would fit well in that phrase that is gramatically correct?
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"If you try to be everything to everyone, you end up being nothing to anyone."
About anyone, Macmillan says:
“Complete nobody” probably is more common as an opposite to “everything to everyone” than is “Nothing to nobody”. Of course the logical opposites of “everything to everyone” include “everything to nobody” and “nothing to anyone” but as noted in Robusto's comment they don't sound as well.
You might consider universally underwhelming
Universal disappointment is another that might fit, along with "unpopular disappointment" (but the latter doesn't have the same meaning as "universal").
"The President set himself out to be everything to everybody, but instead, he was a universal disappointment."
In most cases, the double negative in English is resolved into a positive. This is a case where "nothing to nobody" might be interpreted colloquially to have the meaning you are looking for. In formal writing though, it would be taken with disapproval.