Was Jesus' power limited relative to the belief of others?

Mark 6:5-6 says that Jesus could do no "mighty work". Since the people did not believe, he was unable to save their soul. That was the "mighty work".

He actually did preform an amazing feat "he laid his hands upon a few sick folk, and healed them". The people just did not believe in him "he marvelled because of their unbelief".

Saving the soul is a far more mighty feat than healing somebody's physical body which will get injured again.

I will try to answer this question from within Bible.

As I see it from Bible, some places it is not specifically mentioned that people who were healed had proclaimed their faith in Christ. This is at Mathew: 4:23, Mathew: 12:15, 14.14, Luke: 7:18.

Whereas some places even when there is no faith amongst the audience or the healed person, the healings have taken place. This is evident in the Verses Mathew12.9-13:

Mathew: 12:9 Then Jesus left that place and entered their synagogue. 12:10 A man was there who had a withered hand. And they asked Jesus, “Is it lawful to heal on the Sabbath?” so that they could accuse him. 12:11 He said to them, “Would not any one of you, if he had one sheep that fell into a pit on the Sabbath, take hold of it and lift it out? 12:12 How much more valuable is a person than a sheep! So it is lawful to do good on the Sabbath.” 12:13 Then he said to the man, “Stretch out your hand.” He stretched it out and it was restored, as healthy as the other.

Here in fact the audience certainly was without any faith in Him nor was the healed person expecting so. Similar instances are at Luke 14.1-6, Luke 16.19 etc,

Therefore, from this it can be averred that Jesus' power is not limited or relative to the belief of others. He can demonstrate His love to anyone He wishes to or anyone who wishes to draw close to Him. He was and is always full of power.

But then in verse 6.5, it is said that “Jesus was not able to do any miracles there except the healing of some sick people by laying his hands on them”.

Now as said in this verse He did perform healing of some sick people and those were also miracles. What the verse is saying is that He could not do many miracles except theses ones. He was not able to do any other miracles not because he was not having power to do so but because of their lack of faith and He exercised this option with His own authority not because he lacked power.

Also in the light of Mathew 12.9-13, this becomes clear in the following verse of Luke.

In Luke we see at verse 23:8

“When Herod saw Jesus, he was very glad, for he had long desired to see him, because he had heard about him and was hoping to see him perform some miraculous sign. 23:9 So Herod questioned him at considerable length; Jesus gave him no answer. 23:10 The chief priests and the experts in the law were there, vehemently accusing him. 23:11 Even Herod with his soldiers treated him with contempt and mocked him. Then, dressing him in elegant clothes, Herod sent him back to Pilate.

This gives inkling as to why in some instances, Jesus restricted by His own authority, the demonstration of his healing powers. Here Herod certainly was a man without faith and yet longing to see Jesus perform miracles. For him it was just some sort of public performance of Jesus’ powers. For some instead of filling with faith, they compare it to acts akin to some form of magic or to evil spirit. And we already have this in verse at: Mathew 12:22.

Mathew 12:22 Then they brought to him a demon-possessed man who was blind and mute. Jesus healed him so that he could speak and see. 12:23 All the crowds were amazed and said, “Could this one be the Son of David?” 12:24 But when the Pharisees heard this they said, “He does not cast out demons except by the power of Beelzebul, the ruler of demons!”

Short Answer: No

Complete Answer: The thing we must first understand is that Jesus never used his power on earth, instead he worked in conjunction with God the Father for each and every miracle. We see this time and time again where those healed by him are actually extensions of that person's faith.

Luke 7 New International Version (NIV)

7 When Jesus had finished saying all this to the people who were listening, he entered Capernaum. 2 There a centurion’s servant, whom his master valued highly, was sick and about to die. 3 The centurion heard of Jesus and sent some elders of the Jews to him, asking him to come and heal his servant. 4 When they came to Jesus, they pleaded earnestly with him, “This man deserves to have you do this, 5 because he loves our nation and has built our synagogue.” 6 So Jesus went with them. He was not far from the house when the centurion sent friends to say to him: “Lord, don’t trouble yourself, for I do not deserve to have you come under my roof. 7 That is why I did not even consider myself worthy to come to you. But say the word, and my servant will be healed. 8 For I myself am a man under authority, with soldiers under me. I tell this one, ‘Go,’ and he goes; and that one, ‘Come,’ and he comes. I say to my servant, ‘Do this,’ and he does it.” 9 When Jesus heard this, he was amazed at him, and turning to the crowd following him, he said, “I tell you, I have not found such great faith even in Israel.” 10 Then the men who had been sent returned to the house and found the servant well.

Now how was the man healed, by Jesus or his faith? The correct answer is a bit more complicated than either or. It is actually a bit of both.

If we look back to Genesis 1 and 2 there was nothing between man and God, they had no need for an intermediary, in fact they walked and talked together. Then came the fall, and the necessity of an intermediary between man and God because from the fall to the resurrection we separated ourselves from God. That is why God spoke to the people through prophets and no person could be in the direct presence of God.

In steps Jesus and the whole game changes. Jesus bridged the gap of sin between us and God however to do this he had to "give up" his power on earth because to fulfill the law he has to be fully man (even though he was still fully God on earth as well). Another way to look at this is that Jesus is the embodiment of grace.

Previously to atone for your sins the Jews made sacrifices, after Jesus we have an intercessory who stands in for us. So it is like you (the enemy) having the choice between asking a strong man's most beloved wife or an acquaintance of his to ask the strong man to lift a huge boulder. The question can be righteous but the action is not going to come from the person you are asking but the effectiveness of the person asking for you.

Jesus is that most effective intercessory that bridges the chasm of sin between us and God. Faith is a cornerstone of salvation along with grace and scripture (as it is the word of God). So it makes sense that a group's lack of faith would not warrant any miracles because they are not searching for grace but a handout to continue in sin.