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I have heard it quoted many times in a variety of contexts the following words: "Hashem only gives people what they can handle" or "Hashem never gives people more than they can handle."
I assumed the source of this statement was the Gemarah "Ayn HKB"H ba b'trunyah im briyosav", however, this Gemarah is referring to a different point: God does not demand from a person more than they can do. The idea I am quoting is that God does not give anyone a challenge they cannot overcome, not that God doesn't expect one to overcome an overwhelming challenge.
I'm looking for a source that confirms or denies the statement as I heard it.