Said Rabbi Levi: On that night, the blood of the Passover offering mingled with the blood of circumcision, as it is written: “And I passed over you, and I saw you weltering in your blood; and I said to you, ‘By your blood you shall live!’ and I said to you, ‘By your blood you shall live!’ ” 
Midrash Rabbah, Ruth 6:1
As our sages explain, when G-d came to redeem the Jewish people from their exile in Egypt, He found them “naked of mitzvot.” So He gave them two commandments—the mitzvah of circumcision and the mitzvah of korban pesach (the Passover offering)—so that they should merit the redemption. 
One of the things that these two mitzvot have in common is that they each relate to a particular age or phase in a person’s life. The prescribed time for circumcision is at the age of eight days, soon after the infant’s entry into physical life. The korban pesach was brought by the head of the household—a status a person attains only at an advanced point in his life, after having raised a family and assumed a position of authority in the lives of a significant number of individuals.
Circumcision marks a beginning: a Jew is born, and immediately enters into a covenant that binds his life to G-d. The korban pesach, on the other hand, is brought by a person in mid-life—a person with a past, perhaps even a past that requires re-evaluation and change. Indeed, when instructing the people of Israel to bring the korban pesach, Moses tells them to “retract your hands from idol-worship, and take the lamb,” emphasizing that this mitzvah was to mark a break from their idolatrous past and a redefinition of their lives as servants of G-d.
Our every moment embodies this duality, being both the first moment of the rest of our lives and the culminative moment of all we acheived and experienced up until that point. The challenge to us, as individuals and as a people, is to mingle the “blood of circumcision” with the “blood of the Passover offering”: to combine the freshness of birth with the lessons of maturity, to make our every moment a pristine beginning that, at the same time, is the fruit of a rectified and optimized past.
Based on a public letter by the Rebbe, Nissan 11, 5729 (March 30, 1969)
. Ezekiel 16:6.
. Ibid., verse 7, as per Rashi’s commentary; Midrash Rabbah, Shemot 17:3 and Ruth 6:1; Pirkei d’Rabbi Eliezer, 28:1; et al.
. Another common denominator is that these are the only two mitzvot assei (positive commandments) that carry the penalty of karet.
. Indeed, Maimonides does not consider a child fully born until its eighth day (Guide for the Perplexed, part III, ch. 49).
. See Exodus 12:3-4. While any adult Jew could bring a korban pesach, the laws governing its offering and consumption dictated that it be brought by the head of a large household or extended family. The korban pesach (a yearling lamb or kid) had to be eaten before midnight of Passover eve, and none of its meat was to be left over; only those who were members in the chaburah (“group”) in whose behalf that particular animal was offered were permitted to eat from it; it was supposed to be eaten at the end of the meal, on a full stomach, but not past the point of normal satiety. So for each animal, there had to be a chaburah large enough that nothing would be left over after each of its members ate his small portion—usually no more than the requisite kezayit (approx. 1 oz.). Thus, the head of the chaburah, who brought the korban pesach on its behalf, was usually the head of a large household or extended family (see Mishneh Torah, Laws of the Korban Pesach, 8:3 and Kessef Mishneh, loc cit.).
. Exodus 12:21; Mechilta, ibid.
. Rebbe’s Haggadah, pp. 622-624.