I must first begin by saying that I'm answering from a perspective of a believing Jew. The Torah teaches repeatedly that human sacrifice is something God does not want and finds abhorrent, so the concept that there is any "potential" for a human sacrifice is not there at all. Jesus as a sacrifice for sin is contradictory to the Torah, that alone would invalidate for all time even the most remote possibility of his being a "messiah"...using the Hebrew definition of that word..an anointed ruler.
I didn't come here to contrast Judaism with Christianity, but sometimes in order to explain what it is that Jews believe now or believed in ancient times it is necessary to dispel mistaken notions that appear commonplace and are directly related to what the New Testament says *about* Jewish belief and practice, versus what the Torah and Tanakh directly state.
There is a concept in Christianity *alone* that only blood (animal)sacrifice may atone for sin. That concept has ALWAYS been utterly foreign to the faith of the covenant nation, Israel. Before I can even begin to adequately explain the sacrificial system using the laws of Torah in Leviticus, I must first show that the perspective of Christianity on this issue is dependent on having taken a few key passages out of the Torah and completely out of their context to try to support a human sacrifice as being compatible with the Temple sacrificial system.
Also, rather than reinvent the wheel, I will copy-paste a brief portion from my friend's web page. I sincerely hope you will read the thorough explanation in full there at the link. Rabbi Stuart Federow has read both religion's Bible's and has addressed the differences very well in explaination from a Scriptural perspectifve what it is that Jews believe about things that differ from Christianity. First of all, Jews don't have a concept of "original sin", being born with a burden of sin that must be reconciled. Animal sacrifice has never been the exclusive means to seek atonement. God does not become a man. There is no demi-god Devil in Torah. There is no fall of angels. but for the purposes of this question ..PLEASE read the portion at http://www.whatjewsbelieve.org/ regarding the question that Blood is not necessary for atonement. Jews then and now trust that God will do as promised if we do our part.
Animal sacrifice was never the only way to atonement. *A Korban Chatas (sin sacrifice) was only brought for an accidental transgression of the most severe sins. A Korban Asham Talוi (A sacrifice for doubtful guilt) was only brought if a person was uncertain if they had transgressed a sin for which they were compelled to bring a Korban Chatas.
In the days of borh First and Second Temple, a king or Kohen Gadol (High Priest) had to bring a bull. A normal person (kohen or otherwise) had to bring a female lamb, a poor person brought two birds (either pigeons, doves or swallows- the exact species is subject to debate) and a really poor person brought flour, oil and frankincense.*
There is no blood in flour, oil and frankincense. The important thing was the repentance and the act of showing you had done what was necessary to then ask God to forgive you.
***The centrality of the animal sacrifices ceased, not with the second destruction of the Temple by the Romans, but rather with the first destruction of the Temple by the Babylonians. Please remember that the vast majority of Jews never returned to the Promised Land under Cyrus of Persia. They remained in Babylonia. By the time Jesus was born, eighty percent of the world's Jewish community lived outside of the Promised Land, and could not have cared less about the cessation of the animal sacrifices. When the Temple was reestablished, the Jews of Babylonia made an annual financial gift for the maintenance of the Temple, and the land, but never worried that God was not going to forgive them their sins without a blood sacrifice, just as Diaspora Jews do today. And the reason why they had no such fear, was that the Bible makes it explicitly clear that no blood sacrifice is necessary for the forgiveness of sins, or that the exclusive means for the God-man relationship was through the animal sacrifices.***
Please read at the link below ( topic on the left side of the page) for the scriptural references as to what it is that believing Jews do.
EDIT: With regard to the Second Temple destruction. Some Christians try to tell Jews it was destroyed because we "rejected" Jesus. Here is a bit of background and Biblical/Historic/Jewish perspective that if understood in context, will give a very different viewpoint.
TAMMUZ täˈməz, ancient nature deity worshiped in Babylonia. A god of agriculture and flocks, he personified the creative powers of spring. He was loved by the fertility goddess Ishtar, who, according to one legend, was so grief-stricken at his death that she contrived to enter the underworld to get him back. According to another legend, she killed him and later restored him to life. These legends and his festival, commemorating the yearly death and rebirth of vegetation, corresponded to the festivals of the Phoenician and Greek Adonis and of the Phrygian Attis. The Sumerian name of Tammuz was Dumuzi. In the Bible his disappearance is mourned by the women of Jerusalem (Ezek. 8.14).
Hmm Man/god born of virgin dies and Ishtar resurrects him in the spring...Ishtar ( Easter) spring resurrection...striking isn't it?
Sunrise services in honor of Tammuz and praying for his resurrection is an ancient heathen custom. It is actually described and condemned in the book of Ezekiel.
12. And He said to me, "Have you seen, son of man, what the elders of the house of Israel are doing in the darkness, each one in his paved chambers? For they say, 'The Lord does not see us; the Lord has left the earth.' "
13. And He said to me, "You will yet see again greater abominations that they are doing."
14. And He brought me to the entrance of the gate of the house of the Lord that is to the north, and behold there the women were sitting, weeping for Tammuz.
15. And He said to me, "Have you seen, son of man? You will yet see again greater abominations than these."
16. And He brought me to the inner court of the house of the Lord, and behold, at the entrance of the Temple of the Lord between the porch and the altar, about twenty- five men, their backs to the Temple of the Lord and their faces toward the east, and they were prostrating themselves eastward to the sun.
17. And He said to me, "Have you seen, son of man? Was it [too] trivial to the house of Judah to prevent them from performing the abominations that they have done here? For they have [already] filled the land with violence, and repeatedly provoked Me, and behold they send disgrace into their nose.
18. I too, shall act with fury; My eyes will not spare, neither will I have pity, and they will call into My ears with a loud voice, but I shall not listen to them."
This was a warning prior to the destruction of the FIRST Temple. The Second Temple was destroyed just after another man/god began being worshipped in Jerusalem.
Coincidence?
edit: I think Cher's answer explains things very well.
I hope that together these two answers help others to understand the Jewish view better :)