A friend of mine sent me this question, and I responded, quite a while ago. I happened to re-read my response to her question this morning, and I decided that I had not covered all of the points that should properly be covered in addressing a subject such as this. In light of the things that I have learned since I wrote this, I thought that I could add some new insights to an old question.
Q: Why was the suffering and death of Jesus Christ ENOUGH to atone for the sins of all of us?
A: In the Book of Mormon, the great teacher Amulek taught that "there can be nothing which is short of an infinite atonement which will suffice for the sins of the world" (Alma 34:12). That means that only a sacrifice which endures for eternity, and which is infinite in capacity, can satisfy the debt which each of us has incurred through our transgressions. What is it about Christ, and the atonement which He performed, that made his sacrifice sufficiently infinite to atone for the sins of the world?
Christ kept the whole law (see 1 Peter 2 :21-25 and 1 John 3:4-5 and James 2:10) so he could intercede for us based on his own merits, a claim that no other can make. (See Hebrews 5:8-10) Also, Christ (in concert with God) was acting in accordance with the lawfully prescribed method for expiating sins (by offering himself). (I deliberately chose not to use the term "legally" though one might make the argument that it applies in this instance.) He did so namely by complying with the ordinance that called for the sacrifice of blood to atone for sins (see Exodus 30:10; Leviticus 17:11). Alma 34:11-16 explains this rather well. I refer you also to Hebrews 8:18-22, and Hebrews 9:13-14. Hebrews 10 explains in great detail the ways in which animal sacrifice was only a precursor to and ultimately an inferior shadow of that great and last sacrifice wherein "we are sanctified through the offering of the body of Jesus Christ once for all". Christ’s sacrifice not only surpasses the power and effectiveness of the old law of sacrifice, but it is also in perfect harmony with (and in fact fulfills the requirements of) that same Law, as Paul explains in Hebrews. Paul goes on to explain that the demands of the Law required Christ to make that final redeeming sacrifice by “ the offering of [his] body…once for all” (see Hebrews 10:10) and he declares further that “… by one offering he hath perfected for ever them that are sanctified.” (See Hebrews 10:14).
A study of the epistle to the Hebrews helps us understand that Christ was given authority from God to act as "the great high priest" in administering this the penultimate ordinance of the Law, in which you'll note that a single individual acts in proxy for the whole of God's family. (See Hebrews 7:24-28). As Paul explains in this passage, because Christ "hath an unchangeable priesthood", he is able to save every last person that chooses to come to God through him. He can act in this special capacity as the great high priest because he is "holy, harmless, undefiled, separate from sinners, and made higher than the heavens". His incorruptible nature made his "infinite and eternal" sacrifice superior to those made by mortal priests who had been ordained under the law to perform limited sacrifices for the sins of the people.
In addition, the sheer fact that Christ lives eternally makes it possible for his sacrifice to endure into eternity, or in other word, to be infinite in its effects and power to save mankind, while those mortal priests inevitably died and the sacrifice which they performed had to be renewed by another.
Hebrews 7:25 Wherefore he is able also to save them to the uttermost that come unto God by him, seeing he ever liveth to make intercession for them.
In the act of sacrificing himself (and through the shedding of his blood) Christ (and God) also acted in accordance with and in fulfillment of "the New Covenant" (see Matthew 10:28), that is the promise of redemption and eternal life that God had made to his children from before the foundation of the world. (Titus 1:2). As a part of His plan of redemption, it became necessary for God to make a new covenant with His children (see Hebrews 9:13-14,23).
Behold, the days come, saith the Lord, that I will make a new covenant with the house of Israel, and with the house of Judah: Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the Lord: But this shall be the covenant that I will make with the house of Israel; After those days, saith the Lord, I will put my law in their inward parts [or "mind" as it is quoted by Paul in Hebrews 8:10] and write it in their hearts; and will be their God, and they shall be my people. (Jeremiah 31:31-33)
This so-called “new” covenant was in fact part of God’s plan for his children from the beginning (see Titus 1:2-3), as the promises in the New Covenant had been made to Abraham (see Galatians 3:16) and to his forbears all the way back to Adam. The Old Covenant had only been instituted “because of transgression” after the gospel had been withdrawn from the children of Israel at the time of Moses (see Galatians 3:19; D&C 84:23-27; as well as the above quotation from Jeremiah 31). The conditions and principles contained within the Gospel of Jesus Christ, which include repentance with a broken heart and a contrite spirit (see 3 Nephi 9:19-22), are what make up the terms of the “New Covenant”, which is offered to us through the mediating grace and atoning sacrifice of our Savior. “The Old Covenant” refers to the laws and covenants that God made with his children, which were “added because of transgression”. This is the law of carnal commandments and performances that we have come to associate with Moses. Through Christ we have been given a new covenant, or the Gospel. Christ himself and his sacrifice of himself is God's fulfillment of the new covenant. Living up to the principles and fulfilling the ordinances that make up Christ's Gospel is our responsibility under the new law (see Romans 6:15, 16-18; Ephesians 2:8-10).
There would be no Gospel, or New Covenant without the redeeming sacrifice of the Savior Jesus Christ. Without the ability to repent of our sins, which comes as a gift from the Savior, we would be damned forever. Christ extends the gift of repentance and eternal life freely to all who would partake of it, but he will force it upon no man (Alma 42:27). Through his eternal sacrifice, Christ has made us free to choose life or death: “And they are free to choose liberty and eternal life, through the great Mediator of all men, or to choose captivity and death, according to the captivity and power of the devil…” (see 2 Nephi 2:27) If we choose to reject the gift of repentance, then we choose to accept the consequences of our own sins (see D&C 19:15-19), the main consequence of which is spiritual death (see Romans 6:23) or separation from God (see Helaman 14:17-19). It is solely through the “merits, and mercy and grace” of the Savior (see 2 Nephi 2:6-8) that we can be accounted righteous (see Romans 8:1-4), and it is only through the shedding of his innocent blood that we can be washed clean of all sin. As the Savior states in 3 Nephi 27:19-20, we cannot enter into God’s presence unless we have been washed clean in his blood, and he tells us what it is that we must do if we hope to be sanctified and return to His presence one day.
And no unclean thing can enter into his kingdom; therefore nothing entereth into his rest save it be those who have washed their garments in my blood, because of their faith, and the repentance of all their sins, and their faithfulness unto the end. Now this is the commandment: Repent, all ye ends of the earth, and come unto me and be baptized in my name, that ye may be sanctified by the reception of the Holy Ghost, that ye may stand spotless before me at the last day.
So, in answer to your question, Christ's atonement is "enough" because:
1) Christ kept the entirety of the Law, and so he is the only one who has been "justified" by the Law. He is therefore justified in mercifully interceding on our behalf. He has earned the right through righteousness. (1 John 2:1-2)
2) Because his suffering and death were exactly what was required by law and by covenant as the price for our salvation (see Alma 34:11-16; Hebrews 8:18-22; Hebrews 9:13-14). God promised us that he would make "propitiation for our sins" with his son, because of his infinite love for us. (See 1 John 4:8-10, 17)
3) Christ's sacrifice is infinite and eternal because He is eternal. (Hebrews 7:25, Hebrews 13:8).
4) Christ’s sacrifice is only “enough” for those that:
1) believe in him (Romans 10:9)
2) repent (see Helaman 5:10-11; 14:17-19) with a broken heart and a contrite spirit (2 Nephi 2:6-8)
3) are baptized in His name (John 3:5) and are sanctified by the reception of the Holy Ghost (3 Nephi 27:20)
4) and endure to the end (Matthew 10:22; 3 Nephi 27:16)