彼はできもしないことに手を出した。

English Translation

He bit off more than he could chew.

This is of course not a literal translation.

I guess here でき stands for 溺?
I might be wrong, but if it is so, I imagine a more literal translation could be “He put out a hand in order not to drown”.

I cannot come with a closer proverb, but the meaning does seem a bit different…