Rabbinic literature is loaded with discussions about the importance and greatness of Bris Milah. In many postings, I have alluded to the connection between Bris and Pesach (I will write about this some day). One of the most noticable connections is that Elijah the prophet makes an "appearance" at both.
Here is another connection, as quoted in the Chapters of Rabbi Eliezer (the same one I've quoted a few times recently - just a different section of his comments):
In essence, then, we have a covenant created over blood.
פרקי דרבי אליעזר (היגר) - "חורב" פרק כחבני יעקב מלו את בניהם ואת בני בניהם והנחילם לחק עולם עד שעמד פרעה הרשע וגזר גזירות קשות ומנע להם ברית מילה, וביום שיצאו ישראל ממצרים נמולו כל העם מקטון ועד גדול, שנ' כי מולים היו, והיו ישראל לוקחין דם ברית מילה ונותנין על משקוף בתיהם דם ברית מילה ודם פסח ונתמלא רחמים על ישראל, שנ' ואעבור עליך ואראך מתבוססת בדמיך, בדמך לא כתיב אלא בדמיך, בשני דמים דם ברית מילה ודם פסח, ואומר לך בדמיך חיי, ר' אליעזר אומ' וכי מה ראה הכתוב שני פעמים בדמיך חיי, אלא אמ' הב"ה בזכות דם ברית מילה ובזכות דם פסח נגאלו ממצרים ובזכות דם ברית מילה ובזכות דם פסח אתם עתידים להגאל בסוף מלכות רביעי
The children of Jacob circumcised their children and grandchildren and left them with this practice forever until the wicked Pharaoh rose and made harsh decrees, preventing them from doing Bris Milah (performing the covenantal circumcision). On the day they left Egypt the entire nation was circumcised, from young to old, as it says "Because they were circumcised when they left Egypt" (Joshua 5:5).3. A Covenant of Blood (count continues from previous posting)
The Israelites took the blood of the circumcision and they put that blood and the blood of the Paschal lamb and put them both on the doorposts to become recipients of God's mercy on that fateful night, as it says " And I passed by you and saw you downtrodden with your bloods, and I said to you, 'With your bloods, live,' and I said to you, 'With your bloods, live.' (Ezekiel 16:6). It doesn't say "blood" in the singular, because it refers to two bloods which caused God to skip over the houses that night.
Rabbi Eliezer says, "Why does the verse say 'With your bloods, live' twice? Because the Holy One Blessed be He declared that in the merit of the blood of the covenant and in the merit of the blood of the lamb the Israelites were redeemed from Egypt, and in those same merits they will be redeemed again, at the end of the fourth exile."
In essence, then, we have a covenant created over blood.