Matthew 9:9 As Jesus went on from there, he saw a man named Matthew sitting at the tax collector's booth. "Follow me," he told him, and Matthew got up and followed him.
10 While Jesus was having dinner at Matthew's house, many tax collectors and "sinners" came and ate with him and his disciples. 11 When the Pharisees saw this, they asked his disciples, "Why does your teacher eat with tax collectors and 'sinners'?" 12 On hearing this, Jesus said, "It is not the healthy who need a doctor, but the sick. 13 But go and learn what this means: 'I desire mercy, not sacrifice.' For I have not come to call the righteous, but sinners." NIV
The little ones are without sin: they don't need a saviour yet. You see, Jesus does not need to die for the sinless.
Romans 5:6 You see, at just the right time, when we were still powerless, Christ died for the ungodly. 7 Very rarely will anyone die for a righteous man, though for a good man someone might possibly dare to die. 8 But God demonstrates his own love for us in this: While we were still sinners, Christ died for us. NIV
Does Jesus see children as sinless? I would think so:
Matthew 19:14 Jesus said, "Let the little children come to me, and do not hinder them, for the kingdom of heaven belongs to such as these." 15 When he had placed his hands on them, he went on from there. NIV
As for the overgeneralization: I referred to your understanding of WHY we believe it is essential for salvation, not whether it is.