“In the wilderness of Sinai.” Did they, in fact, die in the wilderness of Sinai? Rather, it teaches that they received their death sentence from Mount Sinai. That is what is written: “Against the noble of the children of Israel, He did not extend His hand” (Exodus 24:11).
Rabbi Pinḥas said: From here [we learn] that they were deserving of the hand being extended [to punish them], as Rabbi Hoshaya said: Did cakes go up with them to Sinai that you say: “They beheld God and ate and drank”? (Exodus 24:11). Rather, it teaches that they feasted their eyes on the Divine Presence. “They beheld God” like a person who looks at another while eating and drinking. Rabbi Yoḥanan said: Actual nourishment, just as it says: “Life is in the light of the king’s countenance” (Proverbs 16:15).
Rabbi Tanḥuma says: It teaches that they acted with arrogance, stood upright and feasted their eyes on the Divine Presence. Rabbi Yehoshua of Sikhnin said in the name of Rabbi Levi: Moses did not feast his eyes on the Divine Presence and benefited from the Divine Presence. He did not feast his eyes on the Divine Presence, as it is written: “Moses concealed his face, because he feared to look at God” (Exodus 3:6).
And benefited from the Divine Presence, as it is written: “Moses did not know that his face was radiant upon His speaking with him” (Exodus 34:29). In reward for “because he feared” (Exodus 3:6), he was privileged to: “They feared to approach him” (Exodus 34:30). In reward for “to look [mehabit]” (Exodus 3:6), he was privileged to: “And beholds [yabit] the image of the Lord” (Numbers 12:8). Nadav and Avihu feasted their eyes on the Divine Presence and received no benefit from it.
Why did they not die at that moment? This is analogous to a king who married [off] his daughter and found in one of the groomsmen a matter of infamy. The king said: ‘If I kill him now, I will compromise my daughter’s celebration. Tomorrow, my celebration will come.
It is preferable during my celebration and not during my daughter’s celebration.’ So, the Holy One blessed be He said: ‘If I kill them now, I will compromise the celebration of the Torah, Tomorrow, My celebration will come. It is preferable during My celebration and not during the celebration of the Torah.’ That is what is written: “On the day of his wedding and on the day of the rejoicing of his heart” (Song of Songs 3:11).
“On the day of his wedding,” this is Sinai, “and on the day of the rejoicing of his heart,” this is the Tent of Meeting.