Leviticus 17:11 is often cited to "prove" that blood atonement is needed to atone for sins. The KJV translates it like this: For the life of the flesh is in the blood: and I have given it to you upon the altar to make an atonement for your souls: for it is the blood that maketh an atonement for the soul.
This interpretation has problems. First, the passage does not say that blood is the only means to atone for souls, and, in fact, Torah lists several other means -- e.g. flour (Lev 5:11), money (Exodus 30:15-16), jewelry (Numbers 31:50) or putting fire from the altar in a censure (Numbers 17:11). In addition, Hosea 14:3 says that our lips (i.e. prayers from our lips) can substitute for bulls (i,.e. blood sacrifice), Micah (6:6-8) says G-d wants a good heart rather than blood sacrifices, and the both Isaiah (1:11) and the Psalmist (40 and 50) say that G-d does not need or care about blood sacrifices. Blood is just one of many means for atonement. (See "Verses Missionaries Ignore" for details.)
Secondly, Leviticus 17:11 speaks of atonement ("kapare" in Hebrew) for our souls, but not for 'sin' -- i.e. an act of intentional wickedness. What else could atonement be for? The Bible evidently has additional uses for the word, because the Bible speaks of atonement for acts committed by mistake (which we do not usually consider sins), and also speaks of making atonement for the altar (Exodus 29:36). The word here may have the implication of making durably holy by applying a coating (see the story of Noah's ark), but whatever the meaning, one cannot impute deliberate wrongdoing to an altar.
One cannot apply this verse to Jesus' blood in any event, because it specifies blood on the altar, and Jesus did not die on any altar, let alone the altar in the Holy Temple in Jerusalem which is clearly the altar Leviticus is referring to.
Finally, the verse is taken out of context. Verses 10 to 14 say (KJV):
10 And whatsoever man there be of the house of Israel, or of the strangers that sojourn among you, that eateth any manner of blood; I will even set my face against that soul that eateth blood, and will cut him off from among his people. 11 For the life of the flesh is in the blood: and I have given it to you upon the altar to make an atonement for your souls: for it is the blood that maketh an atonement for the soul. 12 Therefore I said unto the children of Israel, No soul of you shall eat blood, neither shall any stranger that sojourneth among you eat blood. 13 And whatsoever man there be of the children of Israel, or of the strangers that sojourn among you, which hunteth and catcheth any beast or fowl that may be eaten; he shall even pour out the blood thereof, and cover it with dust. 14 For it is the life of all flesh; the blood of it is for the life thereof: therefore I said unto the children of Israel, Ye shall eat the blood of no manner of flesh: for the life of all flesh is the blood thereof: whosoever eateth it shall be cut off.In other words, the verse has nothing to do with salvation. It is about the dietary laws -- specifically, the comments about the life being in the blood are an explanation for the prohibition against eating blood.