Mourning Nadav and Avihu as a duty for all Israel

בפסוק ואחיכם כל בית ישראל יבכו את השריפה.

On the pasuk: "And your brethren, the entire house of Yisrael, shall weep over the burning" (Vayikra 10:6).

The Sefas Emes opens on the verse following the death of Nadav and Avihu, the sons of Aharon, who were consumed by a heavenly fire. The Torah charges the whole nation — not only Aharon's family — to mourn them.

כנראה שמחויב כל איש ישראל לבכות עליהם כמ"ש בזוה"ק אחרי.

It appears that every individual Jew is obligated to weep over them, as is stated in the holy Zohar, parshas Acharei.

The mourning is not optional or limited to relatives; the Zohar in parshas Acharei teaches that this is a binding obligation upon every Jew, because the loss touches all of Bnei Yisrael.

והענין יתכן לומר כי המה היו צדיקים גמורים וחכמים הגידו כי במקום שבע"ת עומדין אין צדיקים גמורים יכולין לעמוד וא"כ נענשו המה בעבורנו לכן צריכין לבכות עליהם ואין להאריך יותר:

The matter may be explained thus: they were complete tzaddikim, and the Chachamim taught that "in the place where baalei teshuvah (penitents) stand, even complete tzaddikim cannot stand"; if so, they were punished on our account, and therefore we must weep over them — and there is no need to elaborate further.

Nadav and Avihu were perfect tzaddikim. Yet Chazal say that a baal teshuvah reaches a level that even a flawless tzaddik cannot attain. The Sefas Emes hints that these tzaddikim were "burned" — taken from the world — in some measure on behalf of us, the ordinary people who rise through teshuvah. Since their loss was, in a sense, for our sake, every Jew bears a personal obligation to mourn them. He deliberately leaves the deeper point understated.

Summary: Every Jew is obligated to weep over Nadav and Avihu because, though they were complete tzaddikim, the level reached through teshuvah surpasses even theirs — so their death was in some way borne on our behalf, making their mourning a duty for all of Bnei Yisrael.