Robert-
I believe that we have assurance of salvation because of what God himself was able to accomplish:
Now we know that whatever the law says, it says to those who are under the law, so that every mouth may be silenced and the whole world held accountable to God. Therefore no one will be declared righteous in his sight by observing the law; rather, through the law we become conscious of sin.
But now a righteousness from God, apart from law, has been made known, to which the Law and the Prophets testify. This righteousness from God comes through faith in Jesus Christ to all who believe. There is no difference, for all have sinned and fall short of the glory of God, and are justified freely by his grace through the redemption that came by Christ Jesus. God presented him as a sacrifice of atonement, through faith in his blood. He did this to demonstrate his justice, because in his forbearance he had left the sins committed beforehand unpunished - he did it to demonstrate his justice at the present time, so as to be just and the one who justifies those who have faith in Jesus. (Romans 3:19-26,NIV)
and-
What then shall we say? That the Gentiles, who did not pursue righteousness, have obtained it, a righteousness that is by faith; but Israel, who pursued a law of righteousness, has not attained it. Why not? Because they pursued it not by faith but as if it were by works. They stumbled over the "stumbling stone." As it is written:
"See, I lay in Zion a stone that causes men to stumble and a rock that makes them fall, and the one who trusts in him will never be put to shame." (Romans 9:30-33,NIV)
This is the sole foundation of Christianity. In order to progress on the Christian path, we must first accept that we are sinners who have been saved from our shortcomings not through our own efforts, but rather through God's.
The logical next step for us would be to accept a set of laws as our guide, and then resolve to follow that set of laws perfectly. But we humans have a flaw in our psyche that dooms to failure anything we might try to do:
We know that the law is spiritual; but I am unspiritual, sold as a slave to sin. I do not understand what I do. For what I want to do, I do not do, but what I hate I do. And if I do what I do not want to do, I agree that the law is good. As it is, it is no longer I myself who do it, but it is sin living in me. I know that nothing good lives in me, that is, in my sinful nature. For I have the desire to do what is good, but I cannot carry it out. For what I do is not the good I want to do; no, the evil I do not want to do - this I keep on doing. Now if I do what I do not want to do, it is no longer I who do it, but it is sin living in me that does it.
So I find this law at work: When I want to do good, evil is right there with me. For in my inner being I delight in God's law; but I see another law at work in the members of my body, waging war against the law of my mind and making me a prisoner of the law of sin at work within my members. What a wretched man I am! Who will rescue me from this body of death? Thanks be to God - through Jesus Christ our Lord! (Romans 7:14-25a,NIV)
2,000 years after St. Paul wrote this passage psychologists verified the exact flaw he described as being a part of all of our psyches; they gave it the name 'paradoxical intention'. What it 'boils down to' is our total inability to successfully accomplish anything that we try to do. In order for our efforts to be successful, they must come naturally, or they won't come at all. There's even a saying which describes this flaw: "The harder you try, the faster you fail."
Fortunately for us, God has taken this into consideration. Instead of his insisting that we obey innumerable laws which he knows we will fail to successfully do, he implants within us an entirely new nature. This new nature is yet another gift given to us freely as a result of our accepting the salvation which God offers to us:
So I say, live by the Spirit, and you will not gratify the desires of the sinful nature. For the sinful nature desires what is contrary to the Spirit, and the Spirit what is contrary to the sinful nature. They are in conflict with each other, so that you do not do what you want. But if you are led by the Spirit, you are not under law.
The acts of the sinful nature are obvious: sexual immorality, impurity and debauchery; idolatry and witchcraft; hatred, discord, jealousy, fits of rage, selfish ambition, dissensions, factions and envy; drunkenness, orgies, and the like. I warn you, as I did before, that those who live like this will not inherit the kingdom of God.
But the fruit of the Spirit is love, joy, peace, patience, kindness, goodness, faithfulness, gentleness and self-control. Against such things there is no law. Those who belong to Christ Jesus have crucified the sinful nature with its passions and desires. Since we live by the Spirit, let us keep in step with the Spirit. Let us not become conceited, provoking and envying each other. (Galatians 5:16-26,NIV)
So not only does our salvation depend on what God himself has been able to accomplish, but also our proper behavior as Christians depends on what God is still able to accomplish, namely, the implanting within us of a new nature (the fruit of the Spirit). And the reason for both our salvation and our proper behavior as Christians being to God's credit rather than any of it's being to our own is this: By doing it in this manner God has effectively 'slammed the door' on the most dangerous sin of all, namely, the sin of Pride. We cannot boast of our salvation, because in order to obtain that salvation we must accept it as a free gift, totally unearned and undeserved. Further, in order to live our lives in the proper manner as Christians we need to receive another gift, namely, his Spirit's coming to bond with us, and bringing with him this 'fruit of the Spirit', which he implants within us. So all credit is due him, with we ourselves only to be seen as the receivers of his generosity and compassion.
P.S: I myself am Anglican, but the same teaching can be found in nearly all of the 'mainstream' church denominations, such as the Methodist, Presbyterian, Lutheran, and United Church of Christ.