Paul not only felt an obligation to preach the gospel, he also had an eagerness to preach. And I don't think he was just thinking of "preaching" in the only the classic sense. He would share the gospel wherever, whenever, and with whoever he met. No one was to "unimportant" to hear about Christ.
Remember when Jesus was ministering to the crowds He still had an eye for Zacchaeus inn Luke 19, or for the woman with the bleeding problem in Matthew 9:20, or for the "maniac of Gadara" in Mark 5. And with that man in Gadara Jesus had His disciples row across the Sea of Galilee just to reach him, and then they came back.
I remember being impressed with men like Jack Wyrtzen, the founder of the Word of Life Fellowship ministry. Jack would witness to the cab driver on the way to a evangelistic rally. He, like other godly Christian workers, saw no one as too insignificant to minister to.
Are you "ready?" Not only does this mean having an eagerness to share, but do you have the message clear in your mind so you can readily talk with anyone about Jesus? Are you memorizing Scripture? Are you meditating on the Word? Are you praying for a sensitivity to the Spirit of God when He will alert you to the Zacchaeus' in your path?
Paul was glad to be saved. And he was equally glad to share the message of God's power to save with others.