Could any human being save themselves from the penalty and power of Sin? The Bible is unequivocal and plain in answering "No." Our salvation is entirely Christ's domain; he is our Savior and our Salvation, sharing these roles and titles with no one outside of the Godhead (John 14:6; Acts 4:12; 1 Timothy 2:5; 1 John 5:11-12). To our salvation the Bible is also clear we can contribute nothing, which is why we need a Savior. When a person trusts in Christ as their Savior and submits to him as their Lord, they are born a second time, given a new, spiritual identity in Christ, and made a "new creature" in and by him (2 Corinthians 5:17; Romans 8:9-15; Romans 6:1-11; Ephesians 1:1-13, etc.). In other words, they are changed in a very fundamental way, not by their own power, not by contributing to Christ's perfect work, but by the Spirit of Christ alone who baptizes the believer into Christ Jesus, washing and regenerating them spiritually and making them new (Titus 3:5-8; Romans 8:9-13; 1 John 4:13). None of this is in the least contingent upon anything but the willingness of the humble, repentant sinner to believe and receive from Christ his saving work.
So, the believer is profoundly altered when Christ comes to dwell within him, given an entirely new nature by the Holy Spirit. Solely by the Spirit's power is the believer enabled, not just to do God's will, but to desire to do it; the born-again man can only work out what God has first worked into him (or her) by the Spirit (Philippians 2:12b-13). All this is necessary because, apart from God, apart from His enabling power, we can do nothing (John 15:4-5). We come to God "without strength," "foolish, disobedient, deceived, serving various lusts and pleasures, living in malice and envy, hateful and hating one another" (Romans 5:6; Titus 3:5). Prior to salvation, every person is "dead in trespasses and sins," bound under the power of the World, the Flesh and the devil (Ephesians 2:1-3). In such a condition, none of us can contribute in the slightest to saving ourselves. Even our understanding has to be aided by the convicting, illuminating and drawing efforts of the Holy Spirit (John 16:8; 1 Corinthians 2:10-16; John 6:44; 2 Timothy 2:25) in order for us to respond in faith to the truth of the Gospel.
In light of all this, what possible contribution can any of us make to the maintenance of our salvation? Any strength we have spiritually is in God, dwelling in us in the Person of the Holy Spirit more precisely, not in ourselves. In-and-of ourselves, we've got nothing we can contribute to what God has done in saving us, and is doing in making us more and more like Jesus Christ. But some hold that our faith is actually what saves us. So long as one's faith remains strong (whatever that means), one's salvation remains intact. In the minds of some, Jesus only kick-starts salvation; he gets it going for us, but we have to keep it going. Salvation is, then, a partnership, really; our spiritual regeneration is our doing as much as Christ's, in the end. In other words, Jesus has a co-Savior in each one of those who are saved.
To my mind, this is deeply blasphemous stuff. The Bible is crystal clear about how destitute of what was necessary to save ourselves we all were and how, without God, we can only continue to be so after our salvation. Christ is himself the believer's spiritual Life (Colossians 3:4); given what Scripture indicates, it is impossible such life could be located in anything within the believer's own natural capacities. Nonetheless, some want to intrude upon what God did for Man through Christ; they want to elevate themselves such that they can fulfill, or contribute to, or maintain, what only divine perfection and infiniteness could accomplish; they don't want to humble themselves under the truth of their deep impotence and foulness, but defy this reality by way of pious self-effort.
The many proof-texts to which these blasphemous "co-Saviors" refer in support of their blasphemy, aren't, by-and-large warning of lost salvation, but of failing to be saved at all, or of lost fellowship with God. The born-again person who ceases to believe God, to trust in His promises and to count on the truth of who He says they are in Christ, doesn't lose a salvation they had no part in achieving, but is cut-off from the joy, peace and grace of fellowship with God. It is to this fellowship that God's salvation of us is aimed; He wants more than merely to adopt us; His desire is for intimate, daily, direct communion with us. (1 Corinthians 1:9; 2 Corinthians 13:13; 1 John 1:3) This abundant, love-filled, transformative fellowship is supposed to be the ground of, the motivation for, all Christian living. We fall away from all of what could be ours in fellowship with God when we draw back in unbelief from the "exceeding great and precious promises" of God by which we are made "partakers of the divine nature" (2 Peter 1:2-4); we don't, however, lose our redeemed, justified and sanctified status, our salvation, which rests entirely in Jesus (1 Corinthians 1:30).
What freedom, and joy, and peace there is in abandoning the blasphemous, fear-mongering, saved-and-lost, works-salvation ideas that some are so eager to promote! What greater, better motivation there is to be found for holy, Christ-centered living in love and grace than in fear, pride and legalism!