At first blush the answer is obvious... he is, er... Jesus! But the answer becomes more complex when we try to understand the nature of his incarnation. One side might argue that Jesus did his miracles out of his deity. This means that the miracles of Jesus would act as signs of his being deity in the flesh. of course, this is a fact that seems to escape most of the audiences that Jesus ministers to. While they do praise God and acknowledge the great miracles that Jesus is doing among them they see these signs less as a sign of Christ's uniqueness and more as a sign of God working through him. This brings us to the other possibility- that Jesus did his miracles through the same Holy Spirit that you and I have within us. Acts 10.38 seems to indicate that the" anointing of the Holy Spirit and power" is what allowed Jesus to heal and deliver. Jesus himself seems to indicate the same thing in Luke 4.18. This launching of his ministry seems to be linked to the anointing of the Spirit of God. My thinking is that these miracles are less linked with Christ's deity than they are with the deity of the Holy Spirit and the power of God working through him.
As Spirit-baptized believers we see this power as something expected by Jesus (Act 1.8) to come upon all of us. This enduement with power is not a sign of our uniqueness or holiness or spiritual maturity but of God working through us. We have no place for pride or haughtiness, rather we should be humbled that God would choose to use vessels like ourselves. We, as imperfect human vessels, are co-laborers with the Spirit in the anointed work that he has for us.
All the more reason for Spirit filled individuals to be refilled over and over, to make sure that they walk in the power of the Spirit and in the anointing that God has for each of us. There is work for us that powerless religion cannot accomplish!