Just as soon as I master the Trinity I'll explain how God can be sovereign and man can have free will. Like most folks Calvinists sit somewhere on a spectrum of views on the issue. Having read the book Debating Calvinism by Dave Hunt and James White I think White tends towards the Cage-Stage Calvinism and argues that God and God alone is the limiting factor on who enters into Heaven.
I have also heard Steve Brown, another Calvinist, discuss the issue and his view is a little different and makes more sense than most I've heard. He argues that God is totally Sovereign and man has free-will. He says our Aristotelian concept of non-contradiction causes us to says both cannot be true at the same time. I think he is one to something often in the physical universe things take place that are apparent contradictions. If one is unaware of the principles of aerodynamics then it would be a contradiction of the law of gravity to say that heavier than air objects can fly. Yet they do and with greater understanding we can explain why. I think the two concepts appear contradictory, because we are ignorant of something.
Perhaps as eternal beings our actions inside of time our capable of changing circumstances outside of time (or in our thought before time). If there were a way to per se factor time out of the equation is probably would make sense.
In practical application it would be a travesty, dare I say an outright evil, to let any doctrine of election override the great commission. As J Vernon McGee put it: if you could tell the elect by a stripe on their back then you should check before you preach to them; since they don't preach to everybody.
I believe that all that has been created reflects the Creator. Good philosophy follows the truth. However, it seems that most people that engage in arguments for/against Calvinism limit themselves to quoting the Bible.
Here is an interesting article showing how predestination and free will might be reconcilable without violating the non-contradiction principle: