Christ's atoning death is clearly connected with His advocacy before the Father. Therefore, we can see the following truths:
1) It is impossible that the Son would not intercede for everyone for whom He died. If Christ dies as their Substitute, how could He not present His sacrifice in their stead before the Father? Can we really believe that Christ would die for someone that He did not intend to save?
2) It is impossible that anyone for whom the Son did not die could receive Christ's intercession. If Christ did not die in behalf of a certain individual, how could Christ intercede for that individual, since He would have no grounds upon which to seek the Father's mercy?
3) It is impossible that anyone for whom the Son intercedes could be lost. Can we imagine the Son pleading before the Father, presenting His perfect atonement in behalf of an individual that He wishes to save, and the Father rejecting the Son's intercession? The Father always hears the Son (John 11:42). Would He not hear the Son's pleas in behalf of all that the Son desires to save?
Furthermore, if we believe that Christ can intercede for someone that the Father will not save, then we must believe either 1) that there is dissension in the Godhead, the Father desiring one thing, the Son another, or 2) that the Father is incapable of doing what the Son desires Him to do. Both positions are utterly impossible.
That Christ does not act as High Priest for all men is clearly seen in His "High Priestly Prayer" in John 17. The Lord clearly distinguishes between the "world" and those who are His throughout the prayer, and verse 9 makes our point very strongly:I pray for them. I am not praying for the world, but for those you have given me, for they are yours.
When Christ prays to the Father, He does not pray for the "world" but for those that have been given to Him by the Father (John 6:37).
For Whom Did Christ Die?
There are a number of Scriptures that teach us that the scope of Christ's death was limited to the elect. Here are a few of them:Just as the Son of Man did not come to be served, but to serve, and to give his life as a ransom for many (Matthew 20:28).
The "many" for whom Christ died are the elect of God, just as Isaiah had said long before,By his knowledge my righteous servant will justify many, and he will bear their iniquities. (Isaiah 53:11)
The Lord Jesus made it clear that His death was for His people when He spoke of the Shepherd and the sheep:I am the good shepherd. The good shepherd lays down his life for the sheep....just as the Father knows me and I know the Father---and I lay down my life for the sheep (John 10:11, 15).
The good Shepherd lays down His life in behalf of the sheep. Are all men the sheep of Christ? Certainly not, for most men do not know Christ, and Christ says that His sheep know Him (John 10:14). Further, Jesus specifically told the Jews who did not believe in Him, "but you do not believe because you are not my sheep" (John 10:26). Note that in contrast with the idea that we believe and therefore make ourselves Christ's sheep, Jesus says that they do not believe because they are not His sheep! Whether one is of Christ's sheep is the Father's decision (John 6:37, John 8:47), not the sheep's!
[All emphases mine]
You can read the whole thing at Alpha Omega Ministries.