Why is there a separation between that first command given by Moshe of “liktu mimenu ish l’fi ochlo…” and the second command not to leave leftovers until the next day? Why not lump all the instructions together?
The Ohr haChaim later in the parsha (16:22) says an interesting chiddush. When Moshe gave the first instructions the Torah says clearly “Zeh hadavar asher tzivah Hashem,” but when relating the second set of instructions it just says, “Vayomer Moshe…” These second instructions were not Hashem’s words, but were Moshe's. This second command was a product of Moshe's own deductive reasoning. Since a new portion of mon fell every day, Moshe felt that there was no reason to horde one day’s supply and save it for the next day.
When the people disobeyed, the pasuk describes their sin as, “V’lo sham’u el Moshe,” the people did not listen to Moshe. It was Moshe’s charge that they violated, not G-d’s command. Nonetheless, the punishment was no less dire. Miraculously, the leftover mon became spoiled and wormy. Even though G-d did not tell them not to leave over the mon or warn of any consequence for doing so, the fact that Moshe declared this to be the halacha caused the mon to spoil. Hashem ratified Moshe’s sevara and treated it the same as if He had given the tzivuy.
I was thinking that maybe this is what Chazal mean when they talk about “lo nitna Torah elah l’ochlei ha’mon.” Maybe I’m misremembering, but I don’t recall an earlier instance in the Torah where someone is mechadesh a halacha based on the koach of sevara and it becomes a cheftza shel Torah. Built into the parshah of the mon is a hint to the capacity of Klal Yisrael to be mechadesh in Torah.