But Jesus said to him, "Follow Me; and allow the dead to bury their own dead." (Matthew 8:22) Since the physically dead can't bury their own dead, this has to be referring to the spiritually dead.
And when you were dead in your transgressions and the uncircumcision of your flesh, He made you alive together with Him, having forgiven us all our transgressions, (Colossians 2:13)
This is a clear allusion to spiritual death (sin separates us from God) and the resurrection of the spirit to new life through Christ's sacrifice and the forgiveness of sins.
For just as the body without the spirit is dead, so also faith without works is dead. (James 2:26)
We are mere dust without the spirit animating us.
{7} Then the LORD God formed man of dust from the ground, and breathed into his nostrils the breath of life; and man became a living being. Genesis 2:7 (NASB)
This passage from Genesis dovetails nicely with this:
{28} For in him we live, and move, and have our being; as certain also of your own poets have said, For we are also his offspring. Acts 17:28 (KJV)
Even those who reject Christ "live and move and have their being", so this verse is related to the "quickening" of the spirit in all men who accept the sacrifice of Christ for the forgiveness of sins.
The quickening God gave Adam was a spiritual quickening (breathed the spirit into him) followed by a physical quickening (dust to life).
This is the same quickening we receive when we accept Christ:
{1} And you hath he quickened, who were dead [spiritually dead] in trespasses and sins...{4} But God, who is rich in mercy, for his great love wherewith he loved us, {5} Even when we were dead in sins, hath quickened us together with Christ, (by grace ye are saved;) {6} And hath raised us up together, and made us sit together in heavenly places in Christ Jesus: Ephesians 2:1,4-6 (KJV)
Sin separates man from God. Separation from God - the source of our very existence both physically and spiritually - causes spiritual death. The death which follows physically to the unregenerate soul leads to the second death - eternal separation from God.
This is such a fundamental precept of the gospel message that it shouldn't even be the subject of debate among Christians.