"Sinners shall find in my heart the source and infinite ocean of mercy."
Have you ever been so aware of your sinfulness that you believed God could never forgive you? Or perhaps, God will forgive, but God could never really love you as much today as He did before, because of your sin?
Especially near death, when one becomes acutely aware that they will stand before God very soon and render an account for everything they ever did while on earth, many people are tempted to despair of God's mercy. It is truly a temptation; Satan tries to make souls move away from God, making them think that God could never really embrace them, with all of their sins.
But our subjective judgments and feelings ought to be corrected by the objective actions of God. Actions speak louder than words, and what has God done? Over and over, He shows mercy. Even in the Old Testament, God showed Himself abundantly merciful and forgiving. Time and again, God forgave Israel when it sinned against God. He punished Israel, and when Israel suffered and came back to God, God restored Israel.
But in Jesus, God's mercy reaches its perfection in outward manifestation. Jesus is Mercy Itself. The whole reason why the Son of God became man and was born among us was to bring us God's free gift of mercy. In the Gospels, Jesus forgives, forgives, forgives. Even on the cross, He forgives.
Why does Jesus always forgive? Because mercy is a fruit of love. Love is the source of mercy, and His love is summed up in His Sacred Heart. It is an infinite ocean of love we find there, to the extent that, in order to spare man the full strength of divine retribution, the Heart of Jesus took all the punishment we deserved. The Heart of Jesus stood between us and God's wrath, taking the punishment for us. Only an infinite ocean of love could do this. Therefore, how can one despair of God's mercy? Jesus did not come for the righteous, but for the worst of us.