Mark 6:4-6 (NKJV)
But Jesus said to them, "A prophet is not without honor except in his own country, among his own relatives, and in his own house." Now He could do no mighty work there, except that He laid His hands on a few sick people and healed them. And He marveled because of their unbelief. Then He went about the villages in a circuit, teaching.
Only when the gospel is heard and believed does it have power to change lives. Jesus hometown acquaintances were intrigued with his wisdom and teaching but they were unable to believe his words. It was not that Jesus tried to heal and found that He could not do it. It is that God will only act in response to faith. That is why Jesus said that if we have faith as small as a mustard seed we would be able to move mountains. That would not be our power but God's power made willing by our faith.
Jesus was amazed at their unbelief. His hometown friends were too familiar with "good ole Jesus" to recognize Him for who He was. The bible says that familiarity breeds contempt. Perhaps we should check our own level of awe and reverence for the things of God.
Hebrews 11:6 (NKJV)
But without faith it is impossible to please Him, for he who comes to God must believe that He is, and that He is a rewarder of those who diligently seek Him.