What is the Biblical basis that God's sacrifice is sufficient for all of our sins (past included)?

I have always loved the imagery in this verse:

18 Come now, and let us reason together, saith the Lord: though your sins be as scarlet, they shall be as white as snow; though they be red like crimson, they shall be as wool. -- Isaiah 1:18

And Paul, in his epistle to Timothy says

15 This is a faithful saying, and worthy of all acceptation, that Christ Jesus came into the world to save sinners; of whom I am chief. -- Timothy 1:15

Paul also tells us, in his epistle to Titus

14 Who gave himself for us, that he might redeem us from all iniquity, and purify unto himself a peculiar people, zealous of good works. -- Titus 2:14 (emphasis added)

And again, in the epistle to the Hebrews, Paul quotes the prophet Jeremiah, saying:

12 For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more. -- Hebrews 8:12

And last, a personal comment. Just this past week, someone said to me, "God loves broken things. God loves fixing broken things, whether it is a broken heart, a broken mind, a broken spirit, a broken family.... God loves fixing broken things!"

And God, who created the universe and all that is in it, would love to fix your "broken" friend.

In his marvelous book, All of Grace, Charles Spurgeon cites the Apostle Paul in affirming that it is the ungodly people that God justifies, and not the righteous people:

Now to the one who works, his wages are not counted as a gift but as his due. 5 And to the one who does not work but believes in him who justifies the ungodly, his faith is counted as righteousness. Romans 4:4-5 ESV

A common mistake is to believe that Jesus came to save the righteous, but that couldn't be any more wrong that it already is.

God justifies the ungodly--not the righteous. To borrow from a colloquialism, God does not save "the good", but rather "the bad and the ugly."

Jesus Himself stated the same thing:

"I have not come to call the righteous but sinners to repentance.”

And again, Paul claims for himself the title of the chief of sinners:

The saying is trustworthy and deserving of full acceptance, that Christ Jesus came into the world to save sinners, of whom I am the foremost. 1 Timothy 1:15 ESV Luke 5:32 ESV

This is good news to those who identify themselves as ungodly people and sinners, for Christ Jesus came into the world specifically to save us--and to save no one else. He came to save sinners. He came to justify ungodly people. Indeed, anyone who has no sin and is righteous--or believes himself to be that way--that person has no need of justification nor salvation.

"It is the sick who need the doctor--not the healthy." A doctor has no value to a healthy person and is ultimately out of place where there is no disease or impairment. A doctor can only do anything of value to those that have need of him. So, too, the self-righteous Pharisees of Jesus' time felt no need of salvation, so Jesus saved His harshest rebukes for them. Yet, to the adulterer, to the thief, and to the sinner the arms of Jesus were warmly outstretched to receive them.

So, your friend could not be any more qualified to receive salvation from God. In fact, such a person is the perfect fit for the grace and mercy of God. In fact, no one could be a better candidate for salvation than one such as your friend, who understands that he or she is truly a sinner.

(I highly recommend Spurgeon's book, All of Grace, on this subject.)

The question you are asking here is really the essence and the magnificence of the Gospel itself. The scripture that we're all familiar with John 3:16-17

16 “For God loved the world so much that he gave his one and only Son, so that everyone who believes in him will not perish but have eternal life.

17 God sent his Son into the world not to judge the world, but to save the world through him.

Jesus knew what your friend has done when he died on the cross and died for him just the same.

If you are looking for precedence see these examples:

• The Samaritan woman in John 4 - she was not living a moral life yet Jesus takes time to reach out to her.
• The Woman caught in adultery in John 8
• Peter, Jesus' disciple denying him in John 18 and then Jesus restoring him in John 21
• Paul in Acts 8 and 9 - he killed many Christians
• The ultimate example comes in Luke 23:34 when Jesus is on the cross and He forgives the very ones crucifying him.

Jesus even talked about this in a few of His parables for example the lost sheep and the prodigal son.