The מדרש says that the three main miracles that kept בני ישראל alive in the desert wer because of the זכות of the three children of Amram. The מן was given because of משה רבינו, the ענני הכבוד (clouds of glory) were erected because of אהרון הכהן, and the באר מים (well of water) in honor of מרים הנביאה. Each of these miracles actually shows the character traits that symbolize the person in whose honor it was manifested.
The מן was an obvious miracle that even while "hiding" (within the dew cover) showed its greatness while being "modest". It was a miracle that taught the Jewish people a lesson at the same time as sustaining them. It required an acceptance of the protection of Hashem and required faith that it would appear each day while nothing was to be left over for the next day. The בני ישראל had to go out each morning and collect the מן and the ease or difficulty of the collection showed how well each person had learned his lessons. It was also used to show where a person belonged and helped judge disputes. This was the characteristic of משה רבינו in that his greatness was recognized within his modesty and he was the supreme judge and teacher of the people.
The ענני הכבוד were characteristic of אהרון הכהן in that they were an obvious miracle that was erected at teh beginning of the trip and faithfully carried out its duties consistently and without fail. Given the way the מדרש describes the miracles that the clouds performed, we see that they were obvious and did not require any activity from the Children of Israel. It defended them, cleaned their clothes, and smoothed the path. Everything that it did was accomplished in the same miraculous manner at the end as at the beginning. This connects with the description of אהרון in בהעלותך as having lit the candles with the same enthusiasm every day of the trip as at the inauguration of the משכן.
The באר מים actually teaches us more about מרים than the mentions of her in the תורה. During the entire book of שמות we see very little mention about her, but what we do see teaches us the lesson of the באר. In everything she does, she does the minimum necessary to accomplish the task that she sees is necessary and then stays in the background while the job is done. She says the minimum necessary to convince her father to remarry her mother and lift the decree against the rest of בני ישראל having more children. She stands by the river (hidden) to see what would happen to משה and then says the minimum necessary to obtain the "proper" wet nurse for him. She brings the musical instruments to the sea and then lead the other women in playing them so that the entire people can sing the אז ישיר.
This is the way that the miracle of the well is exhibited. There is a single miracle at the beginning, but then it continues in what appears to be a "natural" manner. How many of us think of the miracle of the water flowing from the tap when we turn on the faucet. Similarly, the בני ישראל did not think of the source of the water when they went to the stream coming from the well to get their water every day. It was as if they lived in a permanent oasis. It was only when they lost the well upon her death that they realized what she had done for them over the entire 40 years. This, the loss of the well is what triggered the "song of the well" when it was restored by משה. Now they realized what she had accomplished 40 years before. They realized that if not for her, משה would have had to start a new well at least at every camp site and possibly every day in order to provide them with water. This was the characteristic of מרים, the performance of a task in such a way as to require the minimum of obvious miracles.
We also learn fron the "song of the well" that one does not say the praise for salvation until the complete salvation has occurred. Thus, one does not say the "gomel prayer" until after one has gotten completely healed, finished crossing the desert or the ocean, or been completely released from prison. Thus, the Bnai Yisroel could not sing the song of praise until after they had reached the end of the 40 years of wandering in the desert.
Another interesting point is that it appears (from the מדרשים) that מרים was the only woman to actually die in the desert. It was only the men between the ages of 20 and 60 who were condemned because of the spies. This leads to the question as to why. She was not punished for the "sin" of hitting the rock like משה (she was already dead), she was not condemned for the golden calf or the spies (she was not involved with either of them). There is a דבר תורה that I saw that states that the three of them could not got into the land because the בני ישראל had to be weaned from the miracles in the desert and begin living a "natural" life in the land that they had been given. This is also why Eldad and Medad prophesied that משה would not be allowed to enter the land and יהושע would become the leader. Had the three children of Amram entered the land, the age of miracles would have continued and the Children of Israel could not have made the transition to a "normal" life.
The date of Miriam's death is given as the month in which she died, the exact date of Aharon's death (Rosh Chodesh Av) is given, anfd the date of Moshe's death is not given at all. None of them died as the result of the decree because of the spies. As a result, the TAorah shows that they did not die on Tisha B'Av, which was the date decreed for that punishment. Miriam died in a different month. Aharon died in Av, so the exact date had to be given. Moshe died after the decree had been completed so that his death date did not have to be mentioned at all.
UPDATE: Thanks to ba for pointing out that this last point was stated by the N'tziv