I do not believe that is a fair representation of the Calvinist position. The natural man (1 Cor. 2:14) does not, and cannot, understand the things of the Spirit of God. The inherent problem for the natural man (a.k.a. "sinner") is that he cannot understand the saving message of the Gospel because he "does not accept the things of the Spirit Of God, for they are foolishness to him; and he cannot understand them" (1 Cor. 2:14, NASB). If the natural man, in his natural condition, cannot understand the things of the Spirit of God, something beyond the natural man's ability must take place in order for the natural man to be able to understand and believe the Gospel. I think we see this in Ephesians 2.
"But God, being rich in mercy, because of His great love with which He loved us, even when we were dead in our transgressions, made us alive together with Christ (by grace you have been saved)" (Ephesians 2:4, 5).
God took unilateral action by making a spiritually dead sinner alive, and able to believe. This leads to another topic, namely regeneration before justification, but it reveals how freedom of choice does exist within the Calvinist schema. We choose freely, but only after our nature has been changed by an act of God, independent of our will.