I read a reference to this in Eim Habanim Semeichah, ch. 3,לג (though later editions give R’ Yonatan Eybeschutz’s Ahavat Yonatan here as the source; indeed same phraseology), but there's no source given. I've also heard it from a sichah but he doesn't know which one. I understand that part of the chevlei mashiach is the withering of the quill, that Torah scholars will diminish, but I'm looking for the specific source that Rav Teichtal was referring to, namely that David told Yisrael not everyone will be Torah scholars.
This is brought in Sefer Avkat Rochel by Rabbi Makir ben Yitzchok, sefer rishon in the first sign beginning with the words from Hoshea 3:4:
כִּ֣י ׀ יָמִ֣ים רַבִּ֗ים יֵֽשְׁבוּ֙ בְּנֵ֣י יִשְׂרָאֵ֔ל אֵ֥ין מֶ֙לֶךְ֙ וְאֵ֣ין שָׂ֔ר וְאֵ֥ין זֶ֖בַח וְאֵ֣ין מַצֵּבָ֑ה וְאֵ֥ין אֵפ֖וֹד וּתְרָפִֽים׃
It then goes on to explain that there will be no Roshei Yeshivot or Gaon Yisroel (Gaonim) or faithful leaders or chassidim or kabbalists (Baalei HaShem) at that time.
This first sign was addressing the beginning of the second world war and the rise of the Axis powers.
It should be noted that it doesn’t mean literally there would be none of these individuals, but that they would not be effective (as they traditionally had been in each generation up until then) in protecting the generation from harm, like for example Mordechai and Esther.
This is one of the primary reasons why the previous Lubavitcher Rebbe, Rabbi Yosef Yitzchok Schneerson emphasized that the suffering that took place during the Holocaust was categorically different from anything that had occurred previously.
This Midrash is also found in Beit HaMidrash, Cheder Sheini, page 58, by Aharon Yellinek. It also can be found in volume two of Machzor Vitry.