If we want to be forgiven and cured of sin, disease, hate or any other bad human trait, we just have to give ourselves to Jesus and God, ask forgiveness and work at being better. That is the curing he is talking about. Even mass murderers have Jesus knocking on the door to their hearts, hoping they will answer, and let Jesus in. This takes place as long as we live, and only stops when we die. If a mass murderer gets this attention, how much more should us jaywlking, red light running, and pen lifting people get from Jesus?
Many are invited, but few will be allowed in, because few will answer the door of their heart, and do what Jesus is asking them to do for the Kingdom. Even the mass murderers are invited, but who will answer?