When Jesus is addressing the seven churches in Revelations, he repeats the statement, "to him that overcomes." In Revelation 3:21To him that overcometh will I grant to sit with me in my throne, even as I also overcame, and am set down with my Father in his throne.
See All... Jesus even says, "... to him that overcomes, even as I also overcame..."  My question is; If a person is saved by grace through faith, and the debt is paid in full by the blood of Christ, what is left to overcome? He is calling us to overcome in the same manner as he did, how is that?

I remember worrying over the overcomers myself and I understand your concern. However, I think that if we allow scripture to explain itself, the problem will be solved. We tend to think of overcoming as being entirely victorious in everything. I think God looks at overcoming as being victorious in the end. The one still standing at the end of the day is the victor, no matter how bruised and beaten he may be. And, if we are in Christ, we will overcome in Him and by Him. But let us look at some scriptures.

1 John 4:4Ye are of God, little children, and have overcome them: because greater is he that is in you, than he that is in the world.
See All... states, "Ye are of God, little children, and have overcome them: because greater is he that is in you, than he that is in the world." In this verse, those who are little children have overcome--not because of their own prowess and strength--but because of Him who is in them. We overcome because of the indwelling Christ and not because of our own strength.

Who then are those who overcome? 1 John 5:5Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?
See All... states, "Who is he that overcometh the world, but he that believeth that Jesus is the Son of God?" That sound like all true believers to me.

How then do we all overcome? 1 John 5:4For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith.
See All... says, "For whatsoever is born of God overcometh the world: and this is the victory that overcometh the world, even our faith." We overcome by our faith. If we believe in Christ and are born of God, we overcome.

You mention that our overcoming is to be like that of Christ. Revelation 3:21To him that overcometh will I grant to sit with me in my throne, even as I also overcame, and am set down with my Father in his throne.
See All... states, "To him that overcometh will I grant to sit with me in my throne, even as I also overcame, and am set down with my Father in his throne." I do not think that this verse is comparing the way of our overcoming with the way Christ overcame. Certainly, no one can match the obedience or sufferings of Christ. In part, I believe He is saying that who overcome have done something that Christ also did.

The idea that all the saved are overcomers of a sort should not seem strange to us. Romans 8:37Nay, in all these things we are more than conquerors through him that loved us.
See All... states, "Nay, in all these things we are more than conquerors through him that loved us." How is overcoming anything greater than being more than conquerors? And, when our corruptible shall have put on incorruption, this saying will have come to pass, "Death is swallowed up in victory" (1 Corinthians 15:54So when this corruptible shall have put on incorruption, and this mortal shall have put on immortality, then shall be brought to pass the saying that is written, Death is swallowed up in victory.
See All...). Again, this makes us sound like overcomers.

But, you might ask, do the gifts to the overcomers come to all believers?  Of that I am not sure. It does seem that some of the promised gifts in the messages to the seven churches (Revelation 2-3) might be for outstanding service. Well, it may be that there are overcomers and there are (in some cases) OVERCOMERS. Revelation 2:11He that hath an ear, let him hear what the Spirit saith unto the churches; He that overcometh shall not be hurt of the second death.
See All... promises, "He that overcometh shall not be hurt of the second death." This certainly applies to all true believers.

However, Revelation 2:26And he that overcometh, and keepeth my works unto the end, to him will I give power over the nations:
See All... states, "And he that overcometh, and keepeth my works unto the end, to him will I give power over the nations." This probably refers to overcoming of a special sort. However, we have this also in other passages. 2 Timothy 2:12If we suffer, we shall also reign with him: if we deny him, he also will deny us:
See All... states, "If we suffer, we shall also reign with him." The promise to reign is not given to those who do not suffer.

Our faith in Christ as Saviour makes us overcomers over death, hell, and the grave--as Christ overcame the same. However, I believe there is much yet to overcome in the sense of serving, suffering, and giving our all to Him. Certainly, these OVERCOMERS will receive a greater reward.