What are people denying when they try to earn eternal life by works?
They are denying their total separation from God and their spiritual death in Adam. They refuse to admit that all people are sinners by birth and need Christ's sacrificial death, instead believing their own works can merit God's favor and gain eternal life.
Les explains that when people determine, or try, to make eternal life theirs by their works, they are flatly denying this. They are not admitting that they have been totally separated from God, and they are not admitting that they are dead spiritually. They still think that somehow whatever they do will merit favor with God, and that they are going to get in. The surrounding context shows that all are sinners by virtue of having been born from Adam, and they are separated from God because of Adam. It is not what they have done that makes them sinners; they sin because they are sinners. Christ died for the whole human race because the whole human race needed His sacrificial death and was dead in sin.