An important biblical truth many Christians have overlooked in their evangelistic endeavors is that it's not all on my shoulders to make this person convert. God seals the deal. In his fantastic little book on evangelism, J.I. Packer writes:
It is not right when we regard ourselves as responsible for securing converts, and look to our own enterprise and techniques to accomplish what only God can accomplish. To do that is to intrude ourselves into the office of the Holy Spirit, and to exalt ourselves as the agents of the new birth. And the point that we must see is this: only by letting our knowledge of God's sovereignty control the way in which we plan, and pray, and work in his service, can we avoid becoming guilty of this fault. For where we are not consciously relying on God, there we shall inevitably be found relying on ourselves. And the spirit of self-reliance is a blight on evangelism.
Evangelism and the Sovereignty of God, p. 33-34