Eisegesis is defined as reading into the text what we want it to mean. Bringing our own biases and prejudices to the text will always result in a confused and misguided conclusion. Exegesis is a "reading out" of the scriptures what the scriptures actually say.
Your question assumes two things: the last day in the Bible refers to the end of time; and that Christ's intercession is for everyone. Both of these positions are false.
The last day is defined according to the scriptures first in Gen. 49:1-27 as the latter days of each of the tribes, the sons of Jacob / Israel, the last of which was Judah who was the law giver until the scepter passed to Christ (vs. 10). And when did the scepter pass to Christ?
When did the change pass from the law of Moses to the gospel of Christ? First, when he was baptized of John at the river Jordan before His crucifixion in the 1st century AD. And, finally in full and complete fulfillment at the destruction of that old temple in Jerusalem in AD 70 when He returned in glory to destroy those who sacrificed Him (Rev. 1:7) and persecuted His saints.
In the scriptures the last days were always referring to the last days of the Mosaic covenant and that animal sacrificial temple in Jerusalem which was destroyed in AD 70. It never meant the end of time. It is mankind that have been falsely teaching the end-of-time meaning for centuries. See all of the posts at my blog ShreddingTheVeil.org for the scriptural proofs, especially the ten parts of "It's Not The End of The World' beginning here.
Next, the assumption that the intercession of Jesus is for all is faulty. It is available for all, if... conditional...if we will answer the call to be baptized into Christ, to put on Christ (Matt. 10:32; Rom. 13:14; Gal. 3:27). Once we are in Christ, covered by His blood then His blood substitutionally intercedes for us.
The unbelievers who have rejected Christ do not have this protection. He cannot intercede for those who have not been covered by His substitutionary sacrifice. God will judge those who have rejected His son.
But, judgment is not reserved just for the time of our deaths.
"and as it is laid up to men once to die, and after this -- judgment," (Heb. 9:27, YLT)
Jesus judges continually, and reproves those whom He loves.
"for whom the Lord doth love He doth chasten, and He scourgeth every son whom He receiveth;'" (Heb. 12:6, YLT)
"11 Chastisement of Jehovah, my son, despise not, And be not vexed with His reproof, 12 For whom Jehovah loveth He reproveth, Even as a father the son He is pleased with." (Prov. 3:11-12, YLT)
So, Jesus will place judgments and reproofs upon us while we are yet living on this earth for correction and purification, but each of us will face our final judgment at each of our deaths. If we have been faithful to confess our sins and to repent of them, then God is faithful to forgive us (1 John 1:9). Those in Christ will be passed over out of judgment (John 5:24) and gathered into heaven, and those who rejected Him will be cast out into outer darkness (Matt. 25:30; 2 Pet. 2:17).