Do you see that it is an either or? Either you rely on what you can do to be saved or you rely on what Jesus did to be saved. It cannot be a combination of both. Paul says the same thing later on in the book of Romans, "And if by grace, then it is no longer by works; if it were, grace would no longer be grace." ( Romans 11:6 ). If works could provide salvation for us, then it would make grace meaningless.
Paul is comparing our self-righteousness with true righteousness. If we could be saved by works, then God would have to provide salvation to us as payment for the work done. However, this is an utterly ridiculous argument, because we know that according to Isaiah 64:6, our righteousness apart from Christ is as filthy rags. Not our sin, but our righteousness, those things which we do to obtain right standing with God. So if our righteousness is polluted then according to Romans 6:23, the only wages we would earn is death.
Thankfully Paul does not stop there. He gives us further insight into grace. "However, to the man who does not work but trusts God who justifies the wicked, his faith is credited as righteousness." ( Romans 4:5 ). Paul has been combating the idea that one could be saved by adherence to the law. The Law is not what makes us righteous in the sight of God, our faith is.
Notice in this verse, Paul declares that God justifies the wicked. This was a radical statement to the Jew of this day and also to many who would call themselves Christians today. The ungodly is the only type of person God justifies because that is the only type of person there is to justify. Our wages would earn us death, but the gift of God is what brings about eternal life. ( Romans 6:23 )
If we could work to obtain salvation, then this gift of grace would be meaningless . However grace is not worthless, but precious and priceless. Today, all it takes is the faith like our father Abraham in claiming the promises of God. By doing so, we enter into a standing that is acceptable and pleasing to Him in every way.