Until Adam ate the fruit of the tree he had no sinful desire correct? Would God put such a tree in heaven? Will he forbid us from anything in heaven? I believe there will be no such thing as sin in heaven.
Adam, pre-fall, was also pre-sin nature. It was not until he actually rebelled against God that he did indeed sin. In other words, Adam had a choice.
We, however, do not have a choice. We are born under the curse of God. We are born with a sin nature, hence, it is not our "actions" (or lack thereof) that cause us to become sinners, it is our "position" by birth to which we add the actions of sinful behavior, thought, etc.
That is what is the "big deal" about Christ giving us a "re-birth." We are made new creatures, free men once again, by the imputed righteousness and forensic justification of Christ on our behalf.
Essentially, as positional sinners, we can do nothing at all to "earn" merit from God. We cannot "choose" God. We cannot "please" God. We cannot "do" enough (or anything) that would cause our "position" to change. That requires death.
But, praise God, that death came by His Son, Jesus. Jesus did not die as an "example" or as a "savior" who merely points the way for us to grasp onto and be pulled with Him to eternity. Rather, He satisfied the death penalty for our sin -- becoming our sin -- and in exchange gave us His righteousness. This righteousness was "imputed" to us by a supernatural act of God. We did not merit or earn it. We can not access it by faith or otherwise. It is a gift of God for God's elect, those written in the Lamb's Book of Life before the foundation of the world.
As long as we continue to think that we, somehow, can come to God on some (any!) merit of our own, including faith, we miss the point of the Scriptures that proclaim that we cannot come to God unless God makes it possible. Therefore, both Calvinism and Arminianism (and any derivative thereof) all see God's grace as foremost in the process of becoming a "Christian" -- born again from above, justified, adopted, etc.