What's the Problem, Really?

The Bible declares that all people everywhere need a Savior. But why? What's the problem? One very popular approach to evangelism says that God loves you and has a wonderful plan for your life. The problem, according to this approach, is that man is sinful and separated from God and thus he cannot know and experience God's wonderful plan. But is that really the problem? It's true enough that man is sinful and separated from God, but is the consequence for sin really just missing out on God's best plan for your life? I know a great many people who are willing to endure the separation and settle for something less than God's best. What is the problem, really? How did the Apostle Paul define the issue?