The following is an edited transcription of the audio.
How can God care for a sinner like me?
If you read Psalm 107 you'll notice that it talks about God rescuing people who are in trouble. You'll also notice that a number of them are in trouble because of their own sin. Nevertheless, God comes to them when they cry out to him, and he rescues them over and over again.
So whether you've wrecked your life with drugs, abortion, wrong divorce, multiple marriages, illicit sex, lying, or fraud, you can see from this psalm that those things do not disqualify you from God's rescue. The people in the psalm got themselves into their situations by their own stupidity—rather than someone else's persecution against them—yet God still hears their cry and saves them.
And when you go to the cross you see what it is that makes this kind of mercy possible. The fact that Jesus died in our place, covered all our sin, took all our guilt, removed all our condemnation, and has provided us with a perfection and a righteousness which we could never perform on our own—this is the ground upon which everyone who trusts in him can claim the same mercy from Psalm 107 for themselves. Because of the cross we can know that their own situation right now does not rule us out of God's blessing, favor, and care.
Does God really care for those who have messed their own lives up? If they cry to him, he will come and he will care, because that's what Christ bought for us when he died.