yetziat mitzrayim - Is there a source that says only 1/5th of the Jews will make it past the messiah?

I have heard an explanation, that since only 1/5th of the Jews were liberated from Egypt in the Bible, so too only 1/5th of us Jews will survive the eventual redemption. Is this true, and if it is, what source is there for it?

Answer

Sanhedrin 111a

תניא רבי סימאי אומר נאמר ולקחתי אתכם לי לעם ונאמר והבאתי אתכם מקיש יציאתן ממצרים לביאתן לארץ מה ביאתן לארץ שנים מס' ריבוא אף יציאתן ממצרים שנים מס' ריבוא אמר רבא וכן לימות המשיח שנא' וענתה שמה כימי נעוריה וכיום עלותה מארץ מצרים

It has been taught: R. Simai said: It says, And I will take you to me for a people,’ and it is also said, And I will bring you in [unto the land etc.]. Their exodus from Egypt is thus likened to their entry into the [promised] land: just as at their entry into the [promised] land there were but two out of six hundred thousand, so at their exodus from Egypt there were but two out of six hundred thousand. Raba said: It shall be even so in the days of the Messiah, for it is said, And she shall sing there, as in the days of her youth, and as in the days when she came up out of the land of Egypt.

(Soncino translation)

The Midrash Tanchuma in the beginning of Parshat Beshalach provides the number of 1/5:

וחמשים עלו בני ישראל אחד מחמשה ויש אומרים אחד מחמשים ויש אומרים אחד מחמש מאות רבי נהוראי אומר העבודה לא אחד מחמשת אלפים

And the children of Israel went up armed (chamushim) – one out of five. And some say one out of fifty. And some say one out of five hundred. R. Nehorai says “by golly it was not [even] one out of five thousand!”