Jesus speaks with authority great enough to give and take away physical life. More importantly he has the power give us eternal life, this is why we must listen to him. His words are so powerful that even demons obey him, for example in Mark 1:25 when he commanded the demon to come out of the man, the demon came out. Jesus' authoritative words threatened the pharisees so much that their only alternative to end the threat was to kill him. But the only reason why they did eventually kill him was because he allowed them to. Jesus' authority is not threatened by death because as I said earlier he has authority over life and death. After Jesus died, he rose again.
In order to obtain eternal life you must hear and believe him. Many hear him but do not believe him. They do not believe him because they have no room in their hearts for him. God alone creates room in our hearts for him, but not just a little room, he deserves our entire hearts, in fact he demands that we give every last bit of our hearts to him. We shouldn't refuse him, we should let him clean out our hearts of all our impurities and sin. We should let him, so that we may be fit to enter his kingdom.